Feb. 4, 2014
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The document provides information about an upcoming math test on inequalities and systems of equations. It includes: - A review of topics to be covered on the test like inequalities, parallel and perpendicular lines, and solving systems of equations by graphing, substitution, and elimination. - Sample problems and step-by-step explanations for solving systems of equations using different methods. - A word problem about determining the price of gloves and hats by setting up and solving a system of two equations. The document reviews key concepts and provides practice problems to help students prepare for an upcoming test on inequalities and systems of equations.
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The document provides examples for solving systems of equations through various methods like elimination, substitution, and word problems. It demonstrates setting up systems as equations based on information provided, choosing an elimination method by adding or multiplying equations, isolating variables, substituting values, and checking solutions. Word problems are converted to systems of equations and then solved to find unknown variable values.
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The document outlines the agenda for today which includes a warm-up on systems of equations, reviewing different methods for solving systems of equations like graphing, elimination by addition/subtraction, elimination by multiplying, and substitution. It also provides examples of solving systems of equations using each of these methods and reminds students that Monday will be a review for Tuesday's test and to leave their notebooks before leaving for the day.
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.
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.
Systems of linear equations
The document discusses methods for solving systems of linear equations in two variables, including graphing, elimination, and substitution. It provides examples of using each method to solve systems and determine if they have one solution, no solution, or infinitely many solutions. Key points covered are the three possible outcomes when graphing systems, the steps for the elimination and substitution methods, and how to determine the solution set.
February 18, 2015
The document provides instructions for solving different types of systems of equations through various elimination and substitution methods. It includes examples of systems of equations to solve using addition/subtraction, multiplication, and substitution techniques. It also provides instructions for solving systems of inequalities by graphing and shading the solution regions. Finally, it notes some changes made to the assigned class work problems.
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).
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]
March 28, 2016
The document provides information about assignments and tests for today and upcoming dates. It includes notes about 4th quarter grade trackers, make-up tests during lunch, systems of equations lessons for some periods today and tomorrow, and distributing worksheets. The document also contains math content on solving systems of equations by graphing, substitution, and elimination.
Theory of Equation
1. The document provides an overview of the key concepts in the Theory of Equations unit, including types of equations, methods for solving different types of equations, and properties of roots.
2. It discusses linear equations, simultaneous equations, quadratic equations and their solving methods like elimination, substitution, and factorization.
3. Examples of equation problems from commercial applications are also presented, involving linear, simultaneous and quadratic equations. Worked examples and practice problems are provided for each topic.
Solving systems of Equations by Elimination
The document provides steps for solving systems of equations using the elimination method with addition and subtraction:
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 values back into one equation to find the other variable.
5) Check that the solution satisfies both 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.
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.
June 4, 2014
This document provides a review for an upcoming math test covering several topics:
- Review of addition, subtraction, equations, and an introduction to complex fractions
- Sample problems are provided to review solving quadratic equations algebraically and graphically, as well as rational equations
- Instructions are given for tomorrow's test and how current grades will be calculated, with a proposal that students can pass the quarter by scoring a minimum of 75% on the remaining tests.
November 3, 2014
- The document discusses an upcoming math final exam and provides examples to review rational equations, expressions with fractions, and formulas.
- Topics to review for the final exam include translations, order of operations, integers, and simplifying expressions. Example problems are provided to work through.
- Additional examples cover solving equations with variables on both sides, working with fractional equations, and operations with fractions and decimals such as adding, subtracting, multiplying, and dividing.
February 12, 2015
The document provides information about the following:
1. Today's classwork includes make up tests, completing classwork, and solving systems of equations through elimination, substitution, and word problems.
2. A question is asked about having an extraordinary fear of Friday the 13th, along with definitions of terms in the phobia's name.
3. Examples are shown of determining if an ordered pair is a solution to a given system of equations through substitution.
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 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.
January 29 30
The document provides practice problems on simplifying monomial expressions and dividing monomials. It begins with examples of dividing monomials using the property that when dividing powers with the same base, you subtract the exponents. It then provides practice problems for students to divide monomial expressions and simplify expressions using exponent properties. Sample problems are worked through step-by-step as examples.
Lecture 6.1 6.2 bt
The document outlines the agenda and schedule for a math class. It includes collecting projects, returning exams, homework due dates, and topics to be covered from sections 6.1, 6.2. Exam dates are provided for Exam 5 on April 1st and Exam 6 on April 27th, with the final exam on May 4th. Methods for solving systems of linear equations are reviewed, including graphing, substitution, and elimination methods. Examples are worked through for each method. Classwork and homework assignments are listed at the end.
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2. New concepts are introduced through demonstration by the teacher, then practiced together through examples before students work independently.
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i) The document discusses various methods for solving systems of linear equations, including graphing, substitution, elimination, and cross-multiplication.
ii) It also addresses solving systems that can be reduced to linear equations, such as transforming non-linear equations using substitution.
iii) Examples are provided to illustrate each method for deriving the solution of a system of equations.
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March 30, 2016
The document provides instructions for practicing Khan Academy topics on systems of equations word problems. It also reminds the student to make progress on homework 4.1-4.2 which is due on Friday for full credit. Examples are given for solving systems of equations by substitution and word problems involving jeans/shirts and movie tickets.
March 21, 2016
This document provides information about upcoming tests, review material, and math concepts to be covered in class. It includes:
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The document provides examples and steps for solving systems of inequalities and linear equations. It discusses graphing a single inequality, the steps for graphing systems of inequalities, and provides an example of solving a two-variable linear system of inequalities. Sample problems include determining the number of hours until costs are the same for two plumbing companies and graphing the inequality y < 5x + 1.
April 4, 2016
This document contains a daily agenda and warm-up problems for math class including:
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2) Review of fractions, inequalities, and solving multi-step equations.
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April 6, 2016
The document provides a review of topics related to solving systems of equations and inequalities including:
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2) When graphing systems of inequalities, each line must be drawn and labeled as above, below, or dashed before moving to the next line.
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April 1, 2016
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February 17 2015
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February 18 2016
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February 9 2016
The document outlines an agenda for a math class that includes a warm-up on missed test questions, learning about functions and their domains and ranges, using the vertical line test to determine if a relation is a function, and interpreting graphs. It provides examples of mapping relations to check if they are functions and using the vertical line test. Students are given practice problems to determine if relations are functions and to graph relations and use the vertical line test.
February 10 2016
This document provides instruction on determining the domain and range of functions, identifying functions using mapping and the vertical line test, and interpreting graphs. It includes examples of determining domain and range for various functions defined by equations. Warm-up questions are provided to have students plot points and draw lines from equations. Students are reminded that their class work CW 3.4 is due for full credit.
February 8 2016
The document provides test results and topics for a Khan Academy session on February 14th. It includes the following information:
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Feb. 4, 2014
- 1. February 4, 2014 Today: Review for test and systems of equations < 20 min Test: Inequalities & Lines
- 2. Notes: new people—take the test, do the best you can Write your name on front for now. codes to come Alt.Khan from last week (inequalities) is here. Due on or before next Monday feb. 10 On-line Khan: You can finish last week’s topics by this Sunday for full credit. Pencil only for test, ask if you are not sure of your code. Take 3 minutes to get ready, clear your desk except for scratch paper.
- 3. Inequalities 24x + 2y < - 3 y > -x y< 4 x<3
- 4. Parallel & Perpendicular Lines The equations of two lines are given. Determine the number of solutions. A) None B) One C) Two D) Three E) Infinite Since the lines are not parallel (none), nor are they the same line (infinite), they will, at some point cross. The answer is..
- 5. Review: Systems of Equations (3) Solve the systems of equations by graphing 1 = 1+0 2 + ( + 0) 1 = 3 (2,1) Step 1: Put both equations in slope - intercept form. Step 2: Graph both equations on the same coordinate plane. Step 3: Plot the point where the graphs intersect. Step 4: Check to make sure your solution makes both equations true.
- 6. Review: Systems of Equations (3) Solve the systems of equations by elimination Elimination is easiest when the equations are in standard form. 1: Put the equations in Standard Form. Step 2: Determine which variable to eliminate. Step 3: Add or subtract the equations. Step 4: Plug back in to find the other variable. Step 5: Check your solution. Standard Form: Ax + By = C Look for variables that have the same coefficient. Solve for the variable. Substitute the value of the variable into the equation. Substitute your ordered pair into BOTH equations.
- 7. Review: Systems of Equations (2) 2x + 7y = 31 5x - 7y = - 45 7x + 0 = -14 x = -2 Like variables must be lined under each other. THEN----
- 8. Review: Systems of Equations (2) 2X + 7Y = 31 2(-2) + 7y = 31 -4 + 7y = 31 Substitute your 4 4 answer into either original equation and solve for the second variable. 7y = 35; y = 5 Solution (-2, 5) Now check our answers in both equations---
- 9. Review: Systems of Equations (2) 2x + 7y = 31 2(-2) + 7(5) = 31 -4 + 35 = 31 31 = 31 5x – 7y = - 45 5(-2) - 7(5) = - 45 -10 - 35 = - 45 - 45 =- 45
- 10. Review: Systems of Equations (1) And Finally..... A shopper bought two pairs of gloves and four hats for $43.00. Her friend bought two pairs of gloves and two hats for $30.00. What is the price of each item? Use ‘g’ for gloves and ‘h’ for hats. Equation 1: Equation 2: 2g + 4h = $42.00 2g + 2h = $30.00 Hats are $6.00 each Plug both values in 0g + 2h = $12.00 and check for 2g + 24 = $42.00 equality. 2g = $18.00; g = $9