Solve systemsbygraphing
•Download as PPT, PDF•
0 likes•450 views
A system of equations involves two or more equations with the same variables. When graphing systems of equations, there are three possibilities for the graphs: intersecting lines which have a single solution, parallel lines which have no solution, and coinciding lines which have infinitely many solutions. To solve a system using graphs, graph both equations and find the point of intersection, which is the solution, then check it satisfies both equations.
Report
Share
Report
Share
Recommended
Solve systemsbygraphing
The document discusses solving systems of equations by graphing. It defines a system of equations as two or more equations using the same variables. When graphing systems, there can be three possibilities: intersecting lines which have a single solution where the lines cross; parallel lines which have no solution; or coinciding lines which have infinitely many solutions since the lines overlap. The document provides examples of solving systems by graphing and checking solutions by substituting point values back into the original equations.
Solve systemsbygraphing
This document discusses solving systems of equations by graphing. It defines a system of equations as two or more equations using the same variables, where the solution satisfies all equations. There are three possibilities when graphing systems: intersecting lines, where the intersection point is the solution; parallel lines, where there is no solution; and coinciding lines, where there are infinitely many solutions. It provides examples of each type of system and guides the student through solving sample systems by graphing and checking solutions.
Solving system of Equations by Graphing
The student will learn to solve systems of equations by graphing. There are three types of solutions when graphing two equations: intersecting lines, which have a single solution where the lines cross; parallel lines, which have no solution; and coinciding lines, which have infinitely many solutions since the lines overlap completely. The student will practice graphing systems of equations and identifying the solution based on whether the lines intersect, are parallel, or coincide.
Solving System of Equations by Substitution
1) The document discusses solving systems of equations using substitution. It provides 5 steps for solving a system by substitution: 1) solve one equation for a variable, 2) substitute into the other equation, 3) solve the new equation, 4) plug back in to find the other variable, and 5) check the solution.
2) It then works through examples, showing that substitution is easiest when one equation is already solved for a variable. It also notes that if the final step results in a false statement, there are no solutions, and if true, there are infinitely many solutions.
Solving Systems of Linear Equations by Graphing
Here are the solutions to the systems of equations without graphing:
1. One solution (different slopes)
2. No solution (same slope, different intercepts)
3. One solution (different slopes)
4. No solution (same slope, different intercepts)
5. One solution (different slopes)
6. Infinitely many solutions (same slope and intercept)
7. One solution (different slopes)
8. No solution (same slope, different intercepts)
9. One solution (different slopes)
Solving systems of linear equations by substitution
1) The substitution method for solving systems of linear equations involves solving one equation for one variable and substituting it into the second equation.
2) An example solves the system 2x + y = 4 and 3x + 2y = 7 by solving the first equation for y and substituting it into the second equation.
3) A system can have one solution, infinitely many solutions, or no solutions depending on whether the lines graph the same point, same line, or parallel lines.
Solve Systems By Elimination
1) Put the equations in standard form if needed
2) Determine that y can be eliminated by multiplying the top equation by 3
3) Multiply the top equation by 3 and add it to the bottom equation to eliminate y
4) Solve the resulting equation for the remaining variable
5) Substitute back into one of the original equations to find the other variable
The solution to the system is (1, -2).
Solving Systems of Linear Equations in Two Variables by Graphing
This document discusses solving systems of linear equations in two variables by graphing. It begins by recalling the different types of systems and their properties. It then shows examples of writing linear equations in slope-intercept form and graphing individual equations. The main steps for solving a system by graphing are outlined: 1) write both equations in slope-intercept form, 2) graph them on the same plane, 3) find the point of intersection, and 4) check that the solution satisfies both equations. Several examples are worked through demonstrating how to graph systems, find the point of intersection, and verify the solution. The document concludes with an application problem asking students to solve systems, identify the solution location on a map, and describe the
Recommended
Solve systemsbygraphing
The document discusses solving systems of equations by graphing. It defines a system of equations as two or more equations using the same variables. When graphing systems, there can be three possibilities: intersecting lines which have a single solution where the lines cross; parallel lines which have no solution; or coinciding lines which have infinitely many solutions since the lines overlap. The document provides examples of solving systems by graphing and checking solutions by substituting point values back into the original equations.
Solve systemsbygraphing
This document discusses solving systems of equations by graphing. It defines a system of equations as two or more equations using the same variables, where the solution satisfies all equations. There are three possibilities when graphing systems: intersecting lines, where the intersection point is the solution; parallel lines, where there is no solution; and coinciding lines, where there are infinitely many solutions. It provides examples of each type of system and guides the student through solving sample systems by graphing and checking solutions.
Solving system of Equations by Graphing
The student will learn to solve systems of equations by graphing. There are three types of solutions when graphing two equations: intersecting lines, which have a single solution where the lines cross; parallel lines, which have no solution; and coinciding lines, which have infinitely many solutions since the lines overlap completely. The student will practice graphing systems of equations and identifying the solution based on whether the lines intersect, are parallel, or coincide.
Solving System of Equations by Substitution
1) The document discusses solving systems of equations using substitution. It provides 5 steps for solving a system by substitution: 1) solve one equation for a variable, 2) substitute into the other equation, 3) solve the new equation, 4) plug back in to find the other variable, and 5) check the solution.
2) It then works through examples, showing that substitution is easiest when one equation is already solved for a variable. It also notes that if the final step results in a false statement, there are no solutions, and if true, there are infinitely many solutions.
Solving Systems of Linear Equations by Graphing
Here are the solutions to the systems of equations without graphing:
1. One solution (different slopes)
2. No solution (same slope, different intercepts)
3. One solution (different slopes)
4. No solution (same slope, different intercepts)
5. One solution (different slopes)
6. Infinitely many solutions (same slope and intercept)
7. One solution (different slopes)
8. No solution (same slope, different intercepts)
9. One solution (different slopes)
Solving systems of linear equations by substitution
1) The substitution method for solving systems of linear equations involves solving one equation for one variable and substituting it into the second equation.
2) An example solves the system 2x + y = 4 and 3x + 2y = 7 by solving the first equation for y and substituting it into the second equation.
3) A system can have one solution, infinitely many solutions, or no solutions depending on whether the lines graph the same point, same line, or parallel lines.
Solve Systems By Elimination
1) Put the equations in standard form if needed
2) Determine that y can be eliminated by multiplying the top equation by 3
3) Multiply the top equation by 3 and add it to the bottom equation to eliminate y
4) Solve the resulting equation for the remaining variable
5) Substitute back into one of the original equations to find the other variable
The solution to the system is (1, -2).
Solving Systems of Linear Equations in Two Variables by Graphing
This document discusses solving systems of linear equations in two variables by graphing. It begins by recalling the different types of systems and their properties. It then shows examples of writing linear equations in slope-intercept form and graphing individual equations. The main steps for solving a system by graphing are outlined: 1) write both equations in slope-intercept form, 2) graph them on the same plane, 3) find the point of intersection, and 4) check that the solution satisfies both equations. Several examples are worked through demonstrating how to graph systems, find the point of intersection, and verify the solution. The document concludes with an application problem asking students to solve systems, identify the solution location on a map, and describe the
linear equation system with 2 and 3 variables
The document discusses linear equation systems with 2 and 3 variables. It provides examples of linear equations with 1, 2, and 3 variables. There are 4 methods to solve a system of 2 linear equations: substitution, elimination, elimination-substitution, and graphing. Graphing involves drawing the lines represented by each equation and finding their point of intersection. For 3 variables, one variable is eliminated to obtain 2 equations, which are then solved to find the values for the remaining 2 variables. These values are then substituted back into one of the original equations to solve for the eliminated variable.
Solving Systems by Graphing and Substitution
The document discusses solving systems of linear equations by graphing and substitution. It provides examples of solving systems by graphing, including putting equations in slope-intercept form and finding the intersection point. It also gives examples of solving systems by substitution, including steps like isolating a variable, substituting one equation into the other, solving the resulting equation, and checking solutions. Special cases like no solution and infinitely many solutions are also addressed.
Solving of system of linear inequalities
This document discusses linear inequalities in two variables and their graphical representations. It can be summarized as:
1) A linear inequality in two variables has infinitely many solutions that can be represented on a coordinate plane as all points on one side of a boundary line.
2) The graph of a linear inequality consists of all points in a region called a half-plane, bounded by the boundary line. Points on one side of the line are solutions while points on the other side are not solutions.
3) To solve a system of linear inequalities, the inequalities are graphed on the same grid. The solution set contains all points in the region where the graphs overlap, and any points on solid boundary
Systems equations two varibles
The document discusses solving systems of linear equations graphically. It explains that systems can have one solution, no solution, or infinitely many solutions depending on whether the lines intersect at one point, are parallel, or are the same line. Several examples are worked through showing how to graph the lines and determine the number of solutions. The key steps are: 1) write the equations in slope-intercept form, 2) graph them on the same plane, 3) find where they intersect, and 4) check the solution satisfies both equations.
3.3 graph systems of linear inequalities
This document discusses how to solve systems of linear inequalities by graphing them. It explains that you first put the inequalities into slope-intercept form, then graph each line as dotted or solid based on the inequality symbols and shade the correct region above or below the line. The solution to the system is the region where the graphs overlap. An example demonstrates these steps to find the solution region between two inequalities.
Solving Systems of Linear Equation using Substitution method
This document describes the substitution method for solving systems of linear equations in two variables. It involves solving one equation for one of the variables and substituting that expression into the other equation to find the value of the other variable. The example shows solving the system of equations x + 3y = -4 and x - y = 16 by first solving the first equation for x in terms of y, then substituting that expression into the second equation to solve for y, and finally substituting the value of y back into the original expression for x to find the solution set (-11, -5).
A1, 6 1, solving systems by graphing (rev)
The document defines key terms related to systems of linear equations, including system notation, solution of a system, and methods for determining if an ordered pair is a solution. It provides examples of identifying solutions by substituting values into systems of equations. Graphing methods for solving systems are described, including rewriting equations in slope-intercept form, graphing the lines, and checking the intersection point as the solution.
Solving systems of equations
This document provides an overview of solving systems of equations and inequalities in three methods: graphing, substitution, and elimination. It defines key terms like systems of equations and inequalities. Examples are given to demonstrate each method, including a real-world example about water pitchers. The objectives are listed as solving systems by these three methods and solving systems of inequalities. Benefits of understanding this topic and resources for further information are also outlined.
Fsact6
Here are the key steps to solve systems of linear equations:
1. Write the systems of equations side-by-side in standard form (ax + by = c).
2. Use elimination method:
- Add or subtract corresponding terms from each equation to eliminate one variable.
- Solve the resulting equation for the remaining variable.
- Back-substitute into one of the original equations to solve for the other variable.
3. Use substitution method:
- Solve one equation for one variable in terms of the other.
- Substitute this expression into the other equation and solve for the remaining variable.
- Back-substitute to solve for the first variable.
4. Check that the solutions satisfy both original
Systems Of Equations
This document provides an overview of solving systems of linear equations by graphing. It begins with examples of identifying whether an ordered pair is a solution to a given system. It then explains that the point of intersection between the graphs of two linear equations is the solution to the corresponding system. The document provides examples of solving systems by graphing and checking solutions by substitution. It concludes with a quiz reviewing the concepts taught.
System of linear inequalities
Here is the system of inequalities for the cross-country team problem:
Let x = number of water bottles sold to students
Let y = number of water bottles sold to others
x + y ≤ 100 (they have 100 bottles total)
3x + 5y ≥ 400 (they need at least $400)
Graph the regions defined by these inequalities and the overlapping region is the solution.
9.1 Systems of Linear Equations
This document discusses systems of linear equations and methods for solving them. It defines a linear system as a set of equations where all variables have an exponent of 1. There are three possibilities for a system: 1) a single solution, 2) no solution (inconsistent), or 3) infinitely many solutions. Four methods are presented for solving systems: substitution, elimination, graphing, and matrices. Examples are provided to illustrate substitution and elimination. The document also discusses how to determine if a system is inconsistent or has infinitely many solutions based on the outcome of solving the system.
Solving Systems of Linear Inequalities
This document discusses solving systems of linear inequalities. It begins with examples of graphing two-inequality systems by shading the regions defined by each inequality boundary and finding the overlapping solution region. It also covers checking solutions by testing points. Applications include painting plates within cost and number limits and geometry shapes defined by inequalities. The document emphasizes representing "greater than" or "less than" situations with systems of inequalities and using graphing to find the solution region.
Systems of Linear Equations Graphing
There are three possible outcomes when graphing two linear equations:
1) A single point of intersection, meaning one solution.
2) Parallel lines, meaning no solution.
3) Coincident lines with the same slope and y-intercept, meaning an infinite number of solutions.
The type of solution can be determined without graphing by writing the equations in slope-intercept form and comparing slopes and y-intercepts. Different slopes means one solution, same slope but different intercepts means no solution, and same slope and intercept means infinite solutions.
Solve By Elimination
The document provides steps for solving a system of equations using the elimination method with addition and subtraction. The key steps are: 1) Put both equations in standard form, 2) Determine which variable to eliminate by finding terms with the same coefficients, 3) Add or subtract the equations to eliminate the chosen variable, 4) Substitute the solved variable back into one equation to find the other, and 5) Check the solution by substituting the values into both original equations. Examples are provided to demonstrate applying these steps to solve systems of equations algebraically.
System Of Linear Equations
For a system involving two variables (x and y), each linear equation determines a line on the xy-plane. Because a solution to a linear system must satisfy all of the equations, the solution set is the intersection of these lines, and is hence either a line, a single point, or the empty set
Systems of Linear Equations
The document discusses methods for solving systems of linear equations in two variables, including graphing the lines defined by each equation to find their point of intersection, the elimination method of adding multiples of equations to remove a variable, and the substitution method of solving one equation for one variable and substituting it into the other equation. It provides examples of applying these different solution methods to solve systems of linear equations and determining if a solution exists.
Linear equations rev - copy
A system of linear equations in two variables can be solved either graphically or algebraically. Graphically, the solutions are found by drawing the lines corresponding to each equation and finding their point(s) of intersection. Algebraically, the equations are combined to eliminate one variable, resulting in an equation that can be solved for the remaining variable. A system has a single solution if the lines intersect at one point, no solution if the lines are parallel, or infinite solutions if the lines coincide as the same line.
Mathematics 8 Systems of Linear Inequalities
This learner's module discusses and help the students about the topic Systems of Linear Inequalities. It includes definition, examples, applications of Systems of Linear Inequalities.
Solve Complex Inequalities Algebra 1
The document provides instructions for students to learn how to solve and graph compound inequalities. It explains the differences between using "and" and "or" to join inequalities. Examples are provided where students must graph solutions sets of compound inequalities, identify equivalent expressions, and determine whether a solution is possible based on conflicting inequalities. Key concepts covered include intersecting graphs, unions of solution sets, and using compound inequalities to describe plotted point regions.
Solving for y
The document provides examples of solving linear equations for y and identifying the slope and y-intercept of lines. It includes examples of writing equations in slope-intercept form from given values of slope and y-intercept, as well as writing equations of lines from descriptions. The vocabulary defines slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept.
Slope
This document provides vocabulary and examples for calculating slope and rate of change from coordinate points. It defines slope as rise over run or the change in y over the change in x. Positive slopes lean right, negative slopes lean left, and horizontal and vertical lines have slopes of zero or undefined. Examples calculate the slopes between points, and one example finds the rate of change from a table by calculating the change in the dependent variable over the change in the independent variable.
More Related Content
What's hot
linear equation system with 2 and 3 variables
The document discusses linear equation systems with 2 and 3 variables. It provides examples of linear equations with 1, 2, and 3 variables. There are 4 methods to solve a system of 2 linear equations: substitution, elimination, elimination-substitution, and graphing. Graphing involves drawing the lines represented by each equation and finding their point of intersection. For 3 variables, one variable is eliminated to obtain 2 equations, which are then solved to find the values for the remaining 2 variables. These values are then substituted back into one of the original equations to solve for the eliminated variable.
Solving Systems by Graphing and Substitution
The document discusses solving systems of linear equations by graphing and substitution. It provides examples of solving systems by graphing, including putting equations in slope-intercept form and finding the intersection point. It also gives examples of solving systems by substitution, including steps like isolating a variable, substituting one equation into the other, solving the resulting equation, and checking solutions. Special cases like no solution and infinitely many solutions are also addressed.
Solving of system of linear inequalities
This document discusses linear inequalities in two variables and their graphical representations. It can be summarized as:
1) A linear inequality in two variables has infinitely many solutions that can be represented on a coordinate plane as all points on one side of a boundary line.
2) The graph of a linear inequality consists of all points in a region called a half-plane, bounded by the boundary line. Points on one side of the line are solutions while points on the other side are not solutions.
3) To solve a system of linear inequalities, the inequalities are graphed on the same grid. The solution set contains all points in the region where the graphs overlap, and any points on solid boundary
Systems equations two varibles
The document discusses solving systems of linear equations graphically. It explains that systems can have one solution, no solution, or infinitely many solutions depending on whether the lines intersect at one point, are parallel, or are the same line. Several examples are worked through showing how to graph the lines and determine the number of solutions. The key steps are: 1) write the equations in slope-intercept form, 2) graph them on the same plane, 3) find where they intersect, and 4) check the solution satisfies both equations.
3.3 graph systems of linear inequalities
This document discusses how to solve systems of linear inequalities by graphing them. It explains that you first put the inequalities into slope-intercept form, then graph each line as dotted or solid based on the inequality symbols and shade the correct region above or below the line. The solution to the system is the region where the graphs overlap. An example demonstrates these steps to find the solution region between two inequalities.
Solving Systems of Linear Equation using Substitution method
This document describes the substitution method for solving systems of linear equations in two variables. It involves solving one equation for one of the variables and substituting that expression into the other equation to find the value of the other variable. The example shows solving the system of equations x + 3y = -4 and x - y = 16 by first solving the first equation for x in terms of y, then substituting that expression into the second equation to solve for y, and finally substituting the value of y back into the original expression for x to find the solution set (-11, -5).
A1, 6 1, solving systems by graphing (rev)
The document defines key terms related to systems of linear equations, including system notation, solution of a system, and methods for determining if an ordered pair is a solution. It provides examples of identifying solutions by substituting values into systems of equations. Graphing methods for solving systems are described, including rewriting equations in slope-intercept form, graphing the lines, and checking the intersection point as the solution.
Solving systems of equations
This document provides an overview of solving systems of equations and inequalities in three methods: graphing, substitution, and elimination. It defines key terms like systems of equations and inequalities. Examples are given to demonstrate each method, including a real-world example about water pitchers. The objectives are listed as solving systems by these three methods and solving systems of inequalities. Benefits of understanding this topic and resources for further information are also outlined.
Fsact6
Here are the key steps to solve systems of linear equations:
1. Write the systems of equations side-by-side in standard form (ax + by = c).
2. Use elimination method:
- Add or subtract corresponding terms from each equation to eliminate one variable.
- Solve the resulting equation for the remaining variable.
- Back-substitute into one of the original equations to solve for the other variable.
3. Use substitution method:
- Solve one equation for one variable in terms of the other.
- Substitute this expression into the other equation and solve for the remaining variable.
- Back-substitute to solve for the first variable.
4. Check that the solutions satisfy both original
Systems Of Equations
This document provides an overview of solving systems of linear equations by graphing. It begins with examples of identifying whether an ordered pair is a solution to a given system. It then explains that the point of intersection between the graphs of two linear equations is the solution to the corresponding system. The document provides examples of solving systems by graphing and checking solutions by substitution. It concludes with a quiz reviewing the concepts taught.
System of linear inequalities
Here is the system of inequalities for the cross-country team problem:
Let x = number of water bottles sold to students
Let y = number of water bottles sold to others
x + y ≤ 100 (they have 100 bottles total)
3x + 5y ≥ 400 (they need at least $400)
Graph the regions defined by these inequalities and the overlapping region is the solution.
9.1 Systems of Linear Equations
This document discusses systems of linear equations and methods for solving them. It defines a linear system as a set of equations where all variables have an exponent of 1. There are three possibilities for a system: 1) a single solution, 2) no solution (inconsistent), or 3) infinitely many solutions. Four methods are presented for solving systems: substitution, elimination, graphing, and matrices. Examples are provided to illustrate substitution and elimination. The document also discusses how to determine if a system is inconsistent or has infinitely many solutions based on the outcome of solving the system.
Solving Systems of Linear Inequalities
This document discusses solving systems of linear inequalities. It begins with examples of graphing two-inequality systems by shading the regions defined by each inequality boundary and finding the overlapping solution region. It also covers checking solutions by testing points. Applications include painting plates within cost and number limits and geometry shapes defined by inequalities. The document emphasizes representing "greater than" or "less than" situations with systems of inequalities and using graphing to find the solution region.
Systems of Linear Equations Graphing
There are three possible outcomes when graphing two linear equations:
1) A single point of intersection, meaning one solution.
2) Parallel lines, meaning no solution.
3) Coincident lines with the same slope and y-intercept, meaning an infinite number of solutions.
The type of solution can be determined without graphing by writing the equations in slope-intercept form and comparing slopes and y-intercepts. Different slopes means one solution, same slope but different intercepts means no solution, and same slope and intercept means infinite solutions.
Solve By Elimination
The document provides steps for solving a system of equations using the elimination method with addition and subtraction. The key steps are: 1) Put both equations in standard form, 2) Determine which variable to eliminate by finding terms with the same coefficients, 3) Add or subtract the equations to eliminate the chosen variable, 4) Substitute the solved variable back into one equation to find the other, and 5) Check the solution by substituting the values into both original equations. Examples are provided to demonstrate applying these steps to solve systems of equations algebraically.
System Of Linear Equations
For a system involving two variables (x and y), each linear equation determines a line on the xy-plane. Because a solution to a linear system must satisfy all of the equations, the solution set is the intersection of these lines, and is hence either a line, a single point, or the empty set
Systems of Linear Equations
The document discusses methods for solving systems of linear equations in two variables, including graphing the lines defined by each equation to find their point of intersection, the elimination method of adding multiples of equations to remove a variable, and the substitution method of solving one equation for one variable and substituting it into the other equation. It provides examples of applying these different solution methods to solve systems of linear equations and determining if a solution exists.
Linear equations rev - copy
A system of linear equations in two variables can be solved either graphically or algebraically. Graphically, the solutions are found by drawing the lines corresponding to each equation and finding their point(s) of intersection. Algebraically, the equations are combined to eliminate one variable, resulting in an equation that can be solved for the remaining variable. A system has a single solution if the lines intersect at one point, no solution if the lines are parallel, or infinite solutions if the lines coincide as the same line.
Mathematics 8 Systems of Linear Inequalities
This learner's module discusses and help the students about the topic Systems of Linear Inequalities. It includes definition, examples, applications of Systems of Linear Inequalities.
Solve Complex Inequalities Algebra 1
The document provides instructions for students to learn how to solve and graph compound inequalities. It explains the differences between using "and" and "or" to join inequalities. Examples are provided where students must graph solutions sets of compound inequalities, identify equivalent expressions, and determine whether a solution is possible based on conflicting inequalities. Key concepts covered include intersecting graphs, unions of solution sets, and using compound inequalities to describe plotted point regions.
What's hot (20)
Solving Systems of Linear Equation using Substitution method
Solving Systems of Linear Equation using Substitution method
Viewers also liked
Solving for y
The document provides examples of solving linear equations for y and identifying the slope and y-intercept of lines. It includes examples of writing equations in slope-intercept form from given values of slope and y-intercept, as well as writing equations of lines from descriptions. The vocabulary defines slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept.
Slope
This document provides vocabulary and examples for calculating slope and rate of change from coordinate points. It defines slope as rise over run or the change in y over the change in x. Positive slopes lean right, negative slopes lean left, and horizontal and vertical lines have slopes of zero or undefined. Examples calculate the slopes between points, and one example finds the rate of change from a table by calculating the change in the dependent variable over the change in the independent variable.
Slope intercept & direct variation
This document covers direct variation and slope-intercept form in algebra. It provides examples of direct variation word problems and their equations. It also gives examples of finding the slope and y-intercept of equations in slope-intercept form. Finally, it has students write equations in slope-intercept form from given slope and y-intercept values or word problems.
Inequalities
This document discusses inequalities and their graphs. It defines an inequality as a statement that two expressions are not equal. It explains the symbols used in inequalities like <, >, ≤, and ≥ and how to graph them correctly, with open or closed circles depending on if it's a < or ≤. Examples are provided of writing and graphing simple one-variable inequalities and having the reader practice graphing some on their own. Key points covered include understanding the direction the solution goes based on what side the variable is on and coloring in or leaving open the circle depending on the symbol used.
Multiplying a polynomial by a monomial
This document provides examples for multiplying polynomials by monomials. It begins with warmup problems involving graphing linear equations and finding slopes and y-intercepts. Then, it gives six examples of simplifying polynomial expressions by multiplying polynomials by monomials, such as 5(7n - 2) and 4t^2(3t^2 + 2t - 5).
Unit 1 review
This document reviews key concepts from Unit 1 including: adding, subtracting, multiplying, and dividing integers; order of operations with expressions containing multiple operations; evaluating expressions by substituting values for variables; combining like terms using the distributive property; and determining if proportions are true or false and solving proportions. It provides examples of each concept to practice, with expressions containing integers, variables, operations, and evaluating expressions by substituting numeric values for variables.
GCF
The document provides examples of factoring four-term polynomials and other factoring techniques. It contains 8 examples of factoring polynomials with 4 terms or less like 5x4 + 20x3 + 6x2 + 24x. It also shows other factoring methods like factoring the difference of squares and grouping terms.
More multiplication properties of exponents
This document discusses properties of exponents, including raising a power to a power, such as (am)n = am×n, and raising a product to a power, such as (ab)m = am × bm. It provides examples of simplifying expressions with exponents, such as (a4)7 and (2w)4, using the rules explained. The homework assigned is a worksheet to practice these exponent properties and example simplifications.
Double sided equations
This document provides examples of solving double sided equations in 3 sentences or less. It gives sample equations like 2x + 5 = 3x - 1 and X + 2 = 4x along with their answers. The document encourages trying a few examples on your own and then provides the answers to examples like 5x - 3 = 7x + 5, X = 6, and 2/3 = x, -4 = x.
Adding and subtracting polynomials
This document provides an overview of adding and subtracting polynomials. It defines monomials, binomials, and trinomials as polynomials with 1, 2, or 3 terms respectively. Polynomials can have any number of terms. Terms must have like variables to be combined using addition or subtraction. Examples are provided for determining the type of polynomial, simplifying polynomials by combining like terms, and adding and subtracting polynomials. Practice problems are assigned from the workbook.
Super egg presentation
This document provides two examples of slope calculations. The first example shows a line with points (0,0) and (13,2) which results in a slope of 0. The second example uses points (0,0) and (2,1) which results in an undefined slope. A brief explanation is given that a slope of zero means the line is horizontal while an undefined slope means the line is vertical.
Matrices
This document provides an overview of matrices, including how they are named, the elements within them, and how their dimensions are written. It explains that matrices are arrays of numbers, with elements designated by their row and column position. Square matrices have the same number of rows and columns, while non-square matrices have different numbers of rows and columns. Examples are provided to demonstrate finding specific elements and their locations within matrices of various sizes.
Multiplying polynomials
The document describes three methods for multiplying polynomials:
1) The distributive property, which involves multiplying each term of one polynomial with each term of the other.
2) FOIL (First, Outer, Inner, Last), which is a mnemonic for multiplying binomials by multiplying corresponding terms.
3) The box method, which involves drawing a box and writing one polynomial above and beside the box, then multiplying corresponding terms. Examples are provided to demonstrate each method.
Slope notes
Rate of change and slope allow us to understand the relationship between variables. Rate of change is the change in the dependent variable over the change in the independent variable. Slope is the constant rate of change between two points and is calculated as the rise over the run. Slope can tell us how one quantity changes in relation to another, such as pages read per minute, cost per text, or speed of descent.
8 1 zero and negative exponents-modified
The document discusses exponents and properties of exponents. It provides examples of simplifying expressions with exponents, including expressions with zero and negative exponents. It also covers the multiplication property of exponents, which states that when multiplying powers of the same base, the exponents are added. So for example, am × an = am+n.
Multiplying and-dividing-integers
There are two rules for multiplying and dividing integers:
1) If the integers have the same sign, positive or negative, the answer will be positive.
2) If the integers have different signs, one positive and one negative, the answer will be negative.
A song is provided to help remember the rules, and examples are given to practice applying the rules.
Ratio powerpoint
1) The document discusses ratios and uses Lucky Charms cereal as an example. It states there are 287 marshmallow pieces and 2,583 oat pieces in one box of Lucky Charms.
2) Ratios are introduced as a comparison of two quantities that can be written as a fraction, using "to", or with a colon. The ratio of marshmallows to oats in one box is given as an example.
3) Students practice writing ratios to compare amounts in different scenarios, such as numbers of lions to birds or people to pizzas. They also work on simplifying ratios by writing them in simplest form.
Solving equations
This document discusses solving two-step equations and provides examples of solving equations such as 2x + 1 = 4, X - 2 = 3 + 3, X + 2x = 6, and -x + 4 = 10. The solutions to these example equations are provided as x = 3/2, x = 8, x = 2, and x = -6, respectively.
Viewers also liked (19)
Similar to Solve systemsbygraphing
Solve systemsbygraphing
This document discusses solving systems of equations by graphing. A system of equations contains two or more equations with the same variables. When graphing systems, lines can intersect at a point, be parallel with no solution, or coincide with infinitely many solutions. The document provides examples of each case and instructs students to graph systems, identify the intersection point or lack thereof, and check their answer by substituting values back into the original equations.
3.1 solving systems graphically
The document discusses solving systems of linear equations by graphing. It explains that a system of linear equations contains two or more linear equations using the same variables. To solve a linear system graphically, the two equations must be put into slope-intercept form and graphed on the same coordinate plane. The point where the lines intersect satisfies both equations and is the solution to the system. The solution must be verified by substituting the coordinates into the original equations.
January18
The document provides information about solving systems of linear equations through three main methods: graphing, elimination by addition, and elimination by multiplication. It includes examples of using each method to solve systems with steps shown for substitution and verification of solutions. Practice problems are presented for students to determine the number of solutions from graphs of systems and to solve systems using the elimination methods.
7.1
This document discusses how to solve systems of linear equations by graphing. There are 4 steps: 1) Put both equations in slope-intercept form; 2) Graph both equations on the same coordinate plane; 3) Estimate where the graphs intersect, which is the solution; 4) Check that the solution makes both equations true. It provides examples of solving systems of two linear equations with two variables by graphing them and finding the point where the lines intersect.
Maths
This document discusses linear equations in two variables. It defines linear equations in two variables as equations of the form ax + by = c, where a, b, and c are real numbers and a and b are not both zero. It explains that the graph of any linear equation in two variables is a straight line. It also categorizes different types of systems of linear equations based on the relationship between the lines: intersecting lines have a unique solution; coincident lines have an infinite number of solutions; and parallel lines have no solution. Methods for solving systems of linear equations like substitution, elimination, and graphing are also covered.
Linear Equations
This document discusses solving linear equations in one and two unknowns. It introduces linear equations and their properties. It then describes two methods for solving simultaneous linear equations: substitution and elimination. Examples of both methods are shown step-by-step. Additional online resources for learning these methods are provided.
January 29, 2014
Let x = the smaller number
y = the larger number
Then: x + y = 52 (the sum is 52)
y = 4x + 2 (the larger is 4 times the smaller plus 2)
Substitute the second equation into the first:
x + (4x + 2) = 52
5x + 2 = 52
5x = 50
x = 10
y = 4(10) + 2 = 42
The numbers are 10 and 42.
Linear equations Class 10 by aryan kathuria
This document discusses linear equations and methods to solve systems of linear equations. It defines a linear equation as an equation that can be written in the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not equal to 0. Systems of linear equations can have unique solutions, infinite solutions, or no solutions depending on whether the lines intersect, are coincident, or are parallel. The document describes graphical and algebraic methods to solve systems, including elimination, substitution, and cross-multiplication methods. It provides examples of using each algebraic method to solve systems of two linear equations with two unknowns.
M1 L5 Remediation Notes
This document discusses solving systems of equations and inequalities through three main methods: graphing, substitution, and elimination. It provides examples of each method. For graphing systems, it explains the three possibilities for the graphs: consistent systems with one solution where the lines intersect, inconsistent systems with no solution where the lines are parallel, and dependent systems with infinite solutions where the lines coincide. It then works through examples of using substitution and elimination to solve systems algebraically. [/SUMMARY]
Solving systems of Linear Equations
There are three possible solutions to a system of linear equations in two variables:
One solution: the graphs intersect at a single point, giving the solution coordinates.
No solution: the graphs are parallel lines, making the system inconsistent.
Infinitely many solutions: the graphs are the same line, making the equations dependent.
The substitution method for solving systems involves: 1) solving one equation for a variable, 2) substituting into the other equation, 3) solving the new equation, and 4) back-substituting to find the remaining variable.
February 13, 2015
1. The document outlines the day's math lesson which includes reviewing systems of equations solutions, solving 3x3 systems, and completing yesterday's class work.
2. It provides examples and steps for solving systems of equations by graphing, elimination, and substitution. Equations are presented in standard form and slope-intercept form.
3. Solving 3x3 systems is discussed, noting they cannot be graphed since they exist in three dimensions. The substitution method is demonstrated through an example.
Class 3.pdf
This document discusses solving simultaneous linear equations through algebraic and graphical methods. It covers:
- Algebraic methods like substitution and elimination to solve 2 equations with 2 unknowns.
- Graphing methods to find the point where two lines intersect, representing the solution.
- Conditions where equations have a unique solution, no solution, or infinitely many solutions.
- Extended examples are provided to demonstrate solving 2 and 3 equations with algebraic elimination.
Linear equation in two variables
This project was created by four students - Ananya Gupta, Priya Srivastava, Manisha Negi, and Muskan Sharma from Class IX C at KV OFD Raipur in Dehradun, Uttarakhand. The project discusses linear equations and systems of linear equations, explaining concepts such as slope, y-intercept, dependent and independent equations, and methods for solving systems of linear equations graphically, by substitution, and by elimination.
Linear equations rev
A system of linear equations in two variables can be solved either graphically or algebraically. Graphically involves drawing the lines and finding their point of intersection. Algebraically involves combining the equations to eliminate variables until one is left. A system has a single solution if the lines intersect, no solution if parallel, and infinite solutions if coincident. Algebraic methods include substitution and elimination to solve for the variables.
Pair of linear equations
A system of linear equations in two variables can be solved either graphically or algebraically. Graphically, the solutions are found by drawing the lines corresponding to each equation and finding their point(s) of intersection. Algebraically, the equations are combined to eliminate one variable, resulting in an equation that can be solved for the remaining variable. A system has a single solution if the lines intersect at one point, no solution if the lines are parallel, or infinite solutions if the lines coincide as the same line.
Linear equations
This document provides an overview of linear equations for 8th grade algebra. It defines linear equations as having a constant rate of change. For one variable linear equations, it discusses identifying the different types of solutions (conditional, identity, contradiction) and strategies for solving (isolating the variable). For two variable linear equations, it discusses writing the equation in slope-intercept form, graphing, and determining if an ordered pair is a solution. It then covers systems of linear equations, identifying the different types of systems (independent, inconsistent, dependent) and strategies for solving them (graphing, substitution, elimination).
Analytic Geometry Period 1
The document provides an overview of various topics in analytic geometry, including circle equations, distance equations, systems of two and three variable equations, linear inequalities, rational inequalities, and intersections of inequalities. It defines key concepts, provides examples of how to solve different types of problems, and notes things to remember when working with inequalities.
chapter1_part2.pdf
1. This document discusses linear equations, slope, graphing lines, writing equations in slope-intercept form, and solving systems of linear equations.
2. Key concepts explained include slope as rise over run, the different forms of writing a linear equation, finding the x- and y-intercepts, and using two points to write the equation of a line in slope-intercept form.
3. Examples are provided to demonstrate how to graph lines based on their equations in different forms, find intercepts, write equations from two points, and solve systems of linear equations.
CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT
This document provides information about linear equations in two variables. It defines linear equations and explains that a linear equation in two variables can be written in the form ax + by = c. The document also discusses finding the solutions of linear equations, graphing linear equations, and equations of lines parallel to the x-axis and y-axis. Examples are provided to illustrate key concepts. In the summary, key points are restated such as linear equations having infinitely many solutions and the graph of a linear equation being a straight line.
linear equation in two variable.pptx
- The document discusses linear equations in two variables. It defines linear equations and explains that a linear equation in two variables can be written in the form ax + by = c.
- It describes how linear equations in two variables have infinitely many solutions, represented by pairs of x and y values. The graph of a linear equation in two variables is a straight line.
- The document also discusses how equations of lines parallel to the x-axis or y-axis can be represented. The graph of an equation of the form x = a is a line parallel to the y-axis, while an equation of the form y = a graphs as a line parallel to the x-axis.
Similar to Solve systemsbygraphing (20)
More from chrystal_brinson
All about-my-family
This document provides a brief introduction to the author and their family and background. The author has been teaching math for 17 years including 12 years teaching online. They have a passion for math and their goal is to help others develop a love for math as well.
All about-my-family
This document provides a brief introduction to the author and their family and interests. The author has been teaching math for 16 years including 11 years teaching online. They have a passion for math and their goal is to help others develop a love for math as well.
Expenses
Expenses include needs and wants, with needs being essential items like food, water, and electricity that are required to live, while wants are discretionary items like pets, laptops, and internet that are not essential for survival but desired.
Solving rational equations
The document provides information and examples about solving rational equations. It discusses that a rational equation contains one or more rational expressions. It then provides two main methods for solving rational equations - cross multiplying and finding the least common denominator. Several steps are outlined for using the least common denominator method, including finding the common denominator, clearing denominators by multiplying both sides by the LCM, solving the resulting equation, and checking solutions. Examples of using both methods to solve rational equations are shown. Additional resources for learning more about solving rational equations are also provided.
Solving quadratics by graphing
This document discusses how to solve quadratic equations by graphing. It explains that a quadratic equation is of the form y = ax^2 + bx + c, with a being the quadratic term, b the linear term, and c the constant. The number of real solutions is at most two: one solution, two solutions, or no solutions. Solutions are found by setting the equation equal to 0 and finding the x-intercepts of the graph. The graph of a quadratic is a parabola with the roots as the x-intercepts and the vertex as the maximum or minimum point. Quadratic equations can be graphed by making a table of x and y values to plot the parabola.
All about-my-family
This document provides a brief introduction to the author and their family and pets. The author has been teaching math for 15 years, including 10 years teaching math online, and their goal is to help others love math as much as they do.
Ratio slideshow
The document discusses ratios and how to express them in different formats. Ratios can be expressed using a colon, "to", or as a fraction. They can represent a part-to-part comparison between two parts, or a part-to-whole comparison of a part to the total. Examples are given of simplifying ratios by finding the greatest common factor.
Order of operations
Order of Operations (PEMDAS) provides rules for the sequence of mathematical operations to avoid confusion. It dictates that operations within parentheses should be performed first, followed by exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right. The document provides an overview of the PEMDAS method and examples for the reader to practice applying the order of operations.
All about-my-family
This document provides a brief introduction to the author and their family and pets. The author has 14 years of experience teaching math and has taught online for 9 years, and their passion is helping students love math as well.
Trig notes
This document introduces trigonometric ratios, which compare the sides of a right triangle. It defines the three primary ratios: sine, cosine, and tangent. Sine is the ratio of the opposite side to the hypotenuse. Cosine is the ratio of the adjacent side to the hypotenuse. Tangent is the ratio of the opposite side to the adjacent side. Several examples are provided to demonstrate calculating trigonometric ratios given a right triangle and to find angles or sides using inverse trigonometric functions.
U4 l4 quadratic formula powerpoint
This document provides instruction on solving quadratic equations using the quadratic formula. It explains that the quadratic formula can be used to solve any quadratic equation, even those that cannot be factored. It defines the discriminant (b^2 - 4ac) as an important part of the formula, as the sign of the discriminant determines the number and type of roots. A negative discriminant means there are two complex roots, zero means there is one real root, and a positive discriminant means there are two real roots that can be rational or irrational depending on whether the discriminant is a perfect or non-perfect square. An example problem demonstrates finding the discriminant, describing the roots, and solving a quadratic equation using the formula. Practice
Relations & functions
The document summarizes key concepts about relations and functions including:
1) It defines relation, domain, range, and function.
2) It provides examples of relations that are and are not functions using ordered pairs, tables, and mappings.
3) It shows how to determine if a relation is a function using a vertical line test and mappings.
4) It gives examples of finding the domain and range of relations and determining if other relations are functions.
The y intercept and the slope
This document explains how to graph linear functions in slope-intercept form by plotting the y-intercept and using the slope. It outlines three steps: 1) Plot the y-intercept point on the y-axis. 2) Use the slope to rise up and run over to plot the next point. 3) Connect the dots with a line to graph the function. It also provides extra examples to demonstrate the process.
Solving inequalities one step
Solving inequalities is similar to solving equations, except the inequality sign changes if multiplying or dividing by a negative number. There are multiple numbers that can satisfy an inequality rather than a single solution. Notation for inequalities includes > for greater than, >= for greater than or equal to, < for less than, and <= for less than or equal to. Examples show solving basic linear inequalities involving addition, subtraction, multiplication, and division.
Lesson solving two step equations when -x = #
This document provides instructions for solving two-step equations. It outlines the six key steps: 1) divide the equation with an equal sign, 2) undo addition/subtraction to isolate the variable, 3) simplify, 4) undo multiplication, 5) simplify to solve for the variable, and 6) always check the answer by substituting it back into the original equation. It then provides five practice problems for students to solve.
Solving equations one & two step
1) The document defines terms, constants, coefficients, and discusses how to solve one-step and two-step equations. It provides examples of solving equations involving addition, subtraction, multiplication and division.
2) Sample one-step equations are provided along with the steps to solve each type. Equations involving addition, subtraction, multiplication and division are worked through as examples.
3) A two-step practice problem is given along with the answers. Solving two-step equations is introduced.
Solving one step equations
This document provides examples of how to solve one-step equations by adding, subtracting, multiplying, and dividing. It includes 3 examples for each operation: adding by isolating the variable term on one side of the equation and adding its opposite to both sides; subtracting by isolating the variable term and subtracting its opposite from both sides; multiplying by isolating the variable term and dividing both sides by its coefficient; and dividing by isolating the variable term and multiplying both sides by the reciprocal of its coefficient.
Ratio powerpoint
The document discusses ratios and provides examples using Lucky Charms cereal. It states there are 287 marshmallow pieces and 2,583 oat pieces in one box of Lucky Charms. This ratio of marshmallows to oats can be written in three ways: as a fraction, using the word "to", or using a colon. The document also discusses writing ratios in simplest form and explaining their meanings.
Ratio slideshow
The document discusses ratios and how to express them in different formats. Ratios can be expressed using a colon, "to", or as a fraction. They can compare parts to parts (part-to-part ratios) or parts to the whole (part-to-whole ratios). Examples are given of simplifying ratios by finding the greatest common factor and converting ratios to their simplest form.
Coordinate plane ppt
This document provides notes on plotting points on a coordinate plane, including the location of positive and negative integers on the x and y axes, naming the quadrant that coordinate pairs are located in, and naming the coordinate pair for points in different locations on the plane. It discusses key aspects of the coordinate plane and plotting coordinate pairs to identify points in the different quadrants.
More from chrystal_brinson (20)
Recently uploaded
Enchancing adoption of Open Source Libraries. A case study on Albumentations.AI
Enchancing adoption of Open Source Libraries. A case study on Albumentations.AIVladimir Iglovikov, Ph.D.
Presented by Vladimir Iglovikov:
- https://www.linkedin.com/in/iglovikov/
- https://x.com/viglovikov
- https://www.instagram.com/ternaus/
This presentation delves into the journey of Albumentations.ai, a highly successful open-source library for data augmentation.
Created out of a necessity for superior performance in Kaggle competitions, Albumentations has grown to become a widely used tool among data scientists and machine learning practitioners.
This case study covers various aspects, including:
People: The contributors and community that have supported Albumentations.
Metrics: The success indicators such as downloads, daily active users, GitHub stars, and financial contributions.
Challenges: The hurdles in monetizing open-source projects and measuring user engagement.
Development Practices: Best practices for creating, maintaining, and scaling open-source libraries, including code hygiene, CI/CD, and fast iteration.
Community Building: Strategies for making adoption easy, iterating quickly, and fostering a vibrant, engaged community.
Marketing: Both online and offline marketing tactics, focusing on real, impactful interactions and collaborations.
Mental Health: Maintaining balance and not feeling pressured by user demands.
Key insights include the importance of automation, making the adoption process seamless, and leveraging offline interactions for marketing. The presentation also emphasizes the need for continuous small improvements and building a friendly, inclusive community that contributes to the project's growth.
Vladimir Iglovikov brings his extensive experience as a Kaggle Grandmaster, ex-Staff ML Engineer at Lyft, sharing valuable lessons and practical advice for anyone looking to enhance the adoption of their open-source projects.
Explore more about Albumentations and join the community at:
GitHub: https://github.com/albumentations-team/albumentations
Website: https://albumentations.ai/
LinkedIn: https://www.linkedin.com/company/100504475
Twitter: https://x.com/albumentationsCommunications Mining Series - Zero to Hero - Session 1
This session provides introduction to UiPath Communication Mining, importance and platform overview. You will acquire a good understand of the phases in Communication Mining as we go over the platform with you. Topics covered:
• Communication Mining Overview
• Why is it important?
• How can it help today’s business and the benefits
• Phases in Communication Mining
• Demo on Platform overview
• Q/A
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdf
Monitoring and observability aren’t traditionally found in software curriculums and many of us cobble this knowledge together from whatever vendor or ecosystem we were first introduced to and whatever is a part of your current company’s observability stack.
While the dev and ops silo continues to crumble….many organizations still relegate monitoring & observability as the purview of ops, infra and SRE teams. This is a mistake - achieving a highly observable system requires collaboration up and down the stack.
I, a former op, would like to extend an invitation to all application developers to join the observability party will share these foundational concepts to build on:
“I’m still / I’m still / Chaining from the Block”
“An Outlook of the Ongoing and Future Relationship between Blockchain Technologies and Process-aware Information Systems.” Invited talk at the joint workshop on Blockchain for Information Systems (BC4IS) and Blockchain for Trusted Data Sharing (B4TDS), co-located with with the 36th International Conference on Advanced Information Systems Engineering (CAiSE), 3 June 2024, Limassol, Cyprus.
How to Get CNIC Information System with Paksim Ga.pptx
Pakdata Cf is a groundbreaking system designed to streamline and facilitate access to CNIC information. This innovative platform leverages advanced technology to provide users with efficient and secure access to their CNIC details.
“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...
“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...Edge AI and Vision Alliance
For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/building-and-scaling-ai-applications-with-the-nx-ai-manager-a-presentation-from-network-optix/
Robin van Emden, Senior Director of Data Science at Network Optix, presents the “Building and Scaling AI Applications with the Nx AI Manager,” tutorial at the May 2024 Embedded Vision Summit.
In this presentation, van Emden covers the basics of scaling edge AI solutions using the Nx tool kit. He emphasizes the process of developing AI models and deploying them globally. He also showcases the conversion of AI models and the creation of effective edge AI pipelines, with a focus on pre-processing, model conversion, selecting the appropriate inference engine for the target hardware and post-processing.
van Emden shows how Nx can simplify the developer’s life and facilitate a rapid transition from concept to production-ready applications.He provides valuable insights into developing scalable and efficient edge AI solutions, with a strong focus on practical implementation.Alt. GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using ...
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
20 Comprehensive Checklist of Designing and Developing a Website
Dive into the world of Website Designing and Developing with Pixlogix! Looking to create a stunning online presence? Look no further! Our comprehensive checklist covers everything you need to know to craft a website that stands out. From user-friendly design to seamless functionality, we've got you covered. Don't miss out on this invaluable resource! Check out our checklist now at Pixlogix and start your journey towards a captivating online presence today.
Mind map of terminologies used in context of Generative AI
Mind map of common terms used in context of Generative AI.
Large Language Model (LLM) and it’s Geospatial Applications
Large Language Model (LLM) and it’s Geospatial Applications.
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
Discover how MongoDB Atlas and vector search technology can revolutionize your application's search capabilities. This comprehensive presentation covers:
* What is Vector Search?
* Importance and benefits of vector search
* Practical use cases across various industries
* Step-by-step implementation guide
* Live demos with code snippets
* Enhancing LLM capabilities with vector search
* Best practices and optimization strategies
Perfect for developers, AI enthusiasts, and tech leaders. Learn how to leverage MongoDB Atlas to deliver highly relevant, context-aware search results, transforming your data retrieval process. Stay ahead in tech innovation and maximize the potential of your applications.
#MongoDB #VectorSearch #AI #SemanticSearch #TechInnovation #DataScience #LLM #MachineLearning #SearchTechnology
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
ここ3000字までしか入らないけどタイトルの方がたくさん文字入ると思います。
Securing your Kubernetes cluster_ a step-by-step guide to success !
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
Removing Uninteresting Bytes in Software Fuzzing
Imagine a world where software fuzzing, the process of mutating bytes in test seeds to uncover hidden and erroneous program behaviors, becomes faster and more effective. A lot depends on the initial seeds, which can significantly dictate the trajectory of a fuzzing campaign, particularly in terms of how long it takes to uncover interesting behaviour in your code. We introduce DIAR, a technique designed to speedup fuzzing campaigns by pinpointing and eliminating those uninteresting bytes in the seeds. Picture this: instead of wasting valuable resources on meaningless mutations in large, bloated seeds, DIAR removes the unnecessary bytes, streamlining the entire process.
In this work, we equipped AFL, a popular fuzzer, with DIAR and examined two critical Linux libraries -- Libxml's xmllint, a tool for parsing xml documents, and Binutil's readelf, an essential debugging and security analysis command-line tool used to display detailed information about ELF (Executable and Linkable Format). Our preliminary results show that AFL+DIAR does not only discover new paths more quickly but also achieves higher coverage overall. This work thus showcases how starting with lean and optimized seeds can lead to faster, more comprehensive fuzzing campaigns -- and DIAR helps you find such seeds.
- These are slides of the talk given at IEEE International Conference on Software Testing Verification and Validation Workshop, ICSTW 2022.
UiPath Test Automation using UiPath Test Suite series, part 5
Welcome to UiPath Test Automation using UiPath Test Suite series part 5. In this session, we will cover CI/CD with devops.
Topics covered:
CI/CD with in UiPath
End-to-end overview of CI/CD pipeline with Azure devops
Speaker:
Lyndsey Byblow, Test Suite Sales Engineer @ UiPath, Inc.
Goodbye Windows 11: Make Way for Nitrux Linux 3.5.0!
As the digital landscape continually evolves, operating systems play a critical role in shaping user experiences and productivity. The launch of Nitrux Linux 3.5.0 marks a significant milestone, offering a robust alternative to traditional systems such as Windows 11. This article delves into the essence of Nitrux Linux 3.5.0, exploring its unique features, advantages, and how it stands as a compelling choice for both casual users and tech enthusiasts.
20240605 QFM017 Machine Intelligence Reading List May 2024
Everything I found interesting about machines behaving intelligently during May 2024
Recently uploaded (20)
Enchancing adoption of Open Source Libraries. A case study on Albumentations.AI
Enchancing adoption of Open Source Libraries. A case study on Albumentations.AI
Communications Mining Series - Zero to Hero - Session 1
Communications Mining Series - Zero to Hero - Session 1
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdf
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdf
How to Get CNIC Information System with Paksim Ga.pptx
How to Get CNIC Information System with Paksim Ga.pptx
“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...
“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...
Alt. GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using ...
Alt. GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using ...
20 Comprehensive Checklist of Designing and Developing a Website
20 Comprehensive Checklist of Designing and Developing a Website
Mind map of terminologies used in context of Generative AI
Mind map of terminologies used in context of Generative AI
Large Language Model (LLM) and it’s Geospatial Applications
Large Language Model (LLM) and it’s Geospatial Applications
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
Securing your Kubernetes cluster_ a step-by-step guide to success !
Securing your Kubernetes cluster_ a step-by-step guide to success !
UiPath Test Automation using UiPath Test Suite series, part 5
UiPath Test Automation using UiPath Test Suite series, part 5
Goodbye Windows 11: Make Way for Nitrux Linux 3.5.0!
Goodbye Windows 11: Make Way for Nitrux Linux 3.5.0!
20240605 QFM017 Machine Intelligence Reading List May 2024
20240605 QFM017 Machine Intelligence Reading List May 2024
Solve systemsbygraphing
- 1. Objective The student will be able to: solve systems of equations by graphing.
- 2. What is a system of equations? A system of equations is when you have two or more equations using the same variables. The solution to the system is the point that satisfies ALL of the equations. This point will be an ordered pair. When graphing, you will encounter three possibilities.
- 3. Intersecting Lines The point where the lines intersect is your solution. (1,2) The solution of this graph is (1, 2)
- 4. Parallel Lines These lines never intersect! Since the lines never cross, there is NO SOLUTION! 2 Parallel lines have the Slope = = 2 same slope with different 1 y-intercepts. y-intercept = 2 y-intercept = -1
- 5. Coinciding Lines These lines are the same! Since the lines are on top of each other, there are INFINITELY MANY SOLUTIONS! Coinciding lines have the 2 Slope = = 2 same slope and 1 y-intercepts. y-intercept = -1
- 6. What is the solution of the system graphed below? 1. (2, -2) 2. (-2, 2) 3. No solution 4. Infinitely many solutions
- 7. 1) Find the solution to the following system: 2x + y = 4 x-y=2 Graph both equations. I will graph using x- and y-intercepts (plug in zeros). 2x + y = 4 x–y=2 (0, 4) and (2, 0) (0, -2) and (2, 0) Graph the ordered pairs.
- 8. Graph the equations. 2x + y = 4 2x + (0, 4) and (2, 0) y= 4 x-y=2 y= 2 x– (0, -2) and (2, 0) Where do the lines intersect? (2, 0)
- 9. Check your answer! To check your answer, plug the point back into both equations. 2x + y = 4 2(2) + (0) = 4 x-y=2 Nice job…let’s try another! (2) – (0) = 2
- 10. 2) Find the solution to the following system: y = 2x – 3 -2x + y = 1 Graph both equations. Put both equations in slope-intercept or standard form. I’ll do slope-intercept form on this one! y = 2x – 3 y = 2x + 1 Graph using slope and y-intercept
- 11. Graph the equations. y = 2x – 3 m = 2 and b = -3 y = 2x + 1 m = 2 and b = 1 Where do the lines intersect? No solution! Notice that the slopes are the same with different y-intercepts. If you recognize this early, you don’t have to graph them!
- 12. Check your answer! Not a lot to check…Just make sure you set up your equations correctly. I double-checked it and I did it right…
- 13. What is the solution of this system? 3x – y = 8 2y = 6x -16 1. (3, 1) 2. (4, 4) 3. No solution 4. Infinitely many solutions
- 14. Solving a system of equations by graphing. Let's summarize! There are 3 steps to solving a system using a graph. Graph using slope and y – intercept Step 1: Graph both equations. or x- and y-intercepts. Be sure to use a ruler and graph paper! This is the solution! LABEL the Step 2: Do the graphs intersect? solution! Substitute the x and y values into Step 3: Check your solution. both equations to verify the point is a solution to both equations.