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The document discusses linear equations in two variables. It defines linear equations as equations containing two variables where each variable has an exponent of 1. It provides examples and discusses the general form of simultaneous linear equations as a1x + b1y = c1 and a2x + b2y = c2. The document also discusses framing linear equations from word problems, graphically representing solutions, criteria for consistent/inconsistent systems, and methods for algebraically solving simultaneous linear equations including elimination, substitution, and cross multiplication.

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Coordinate geometry

Coordinate geometry describes the position of points on a plane using an ordered pair of numbers (x, y). It was developed by French mathematician René Descartes in the 1600s. The system uses two perpendicular axes (the x-axis and y-axis) that intersect at the origin point (0,0). Values to the right of the x-axis and above the y-axis are positive, while values to the left and below are negative. The plane is divided into four quadrants by these axes.

Linear equations in two variables

This presentation include various methods of solving linear equations like substitution, elimination and cross-multiplication method.

Algebraic expressions

This document provides an overview of algebraic expressions. It defines variables and algebraic expressions, and explains that expressions can be evaluated when the variable is defined. Examples are given to show how expressions represent relationships between quantities. Words that indicate addition, subtraction, multiplication and division are listed. Practice problems are included to write expressions for word phrases and situations. The key aspects covered are variables, expressions, evaluating expressions, and writing expressions from word problems.

11.2 graphing linear equations in two variables

The document discusses how to graph linear equations and inequalities in two variables. It provides examples of graphing linear equations by plotting ordered pairs, finding intercepts, and using linear equations to model data. Specifically, it shows how to graph equations of the form y=mx+b, Ax+By=0, y=b, and x=a. It demonstrates finding intercepts and using them to graph equations. Finally, it gives an example of using a linear equation to model the monthly costs of a small business based on the number of products sold.

Algebraic expressions and identities

This document defines important terms related to algebraic expressions and polynomials. It explains that expressions are formed using variables and constants, and terms are added to form expressions. A monomial has one term, a binomial has two terms, and a trinomial has three terms. A polynomial can have any number of terms. Like terms have the same variables with the same powers, while unlike terms do not. The document also describes how to add, subtract, and multiply algebraic expressions and polynomials, and lists four standard identities.

Real numbers- class 10 mathematics

this is a short ppt but it will give you basic information about real numbers and enhance you mathematics skills.

Solving Quadratic Equations by Factoring

The document discusses solving quadratic equations by factoring. It provides examples of factoring quadratic expressions to find the solutions to the equations. These include using the zero product rule, factoring a common factor, and factoring a perfect square. It also provides two word problems involving consecutive integers and the Pythagorean theorem and shows how to set up and solve the quadratic equations derived from the word problems.

Completing the square

This document provides examples and instructions for solving quadratic equations by completing the square. It begins with examples of solving quadratic equations using the square root property. It then explains how to complete the square to write a quadratic expression as a perfect square trinomial. Examples are provided to demonstrate completing the square and using it to solve quadratic equations. The document ensures readers understand completing the square through check examples and objectives.

Maths ppt linear equations in two variables

AN EQUATION WHICH CAN BE WRITTEN IN THE FORM OF ax+by+c=0 WHERE a,b and c ARE REAL NUMBERS.
YOU WILL GET TO KNOW HOW TO REPRESENT THE EQUATIONS IN A GRAPH.

PPT 7th grade math

The document discusses linear relationships and how to identify them using tables of x and y values or graphs. It provides examples of determining if a relationship is linear by looking for a common relationship between the x and y values that creates a straight line graph. It also discusses using formulas in slope-intercept form (y=mx+b) to identify linear relationships based on whether the formula fits that form and what the y-intercept value (b) would be.

Quadratic Formula Presentation

The document introduces two methods for solving quadratic equations - factoring and graphing. It provides examples of equations that cannot be solved using these methods. It then introduces the quadratic formula as the method to use for equations that cannot be factored or graphed easily. It walks through identifying the a, b, and c coefficients needed for the quadratic formula. It provides examples of using the formula and encourages practicing with a worksheet.

MATHS - Linear equation in two variable (Class - X) Maharashtra Board

MATHS - Linear equation in two variable
(Class - X)
Maharashtra Board
Equations/Expressions
Word Problem

Class IX Linear Equations in Two Variables

This document provides an introduction to linear equations in two variables. It defines a linear equation in two variables as one 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 both zero. Examples are given of writing equations in this form and identifying the values of a, b, and c. The document also discusses that a linear equation in two variables has infinitely many solutions, which can be represented as ordered pairs (x,y) that satisfy the equation.

Graphing linear equations

There are three main forms for writing linear equations: slope-intercept form (y=mx+b), point-slope form (y-y1=m(x-x1)), and standard form (Ax + By = C). Each form can be used to graph the line by finding ordered pairs that satisfy the equation and plotting those points. For slope-intercept form, a table of x-values with their corresponding y-values is made to find the points. For point-slope form and standard form, the given point and slope or intercepts are used to find another point which are then plotted and connected with a line.

Solving Linear Equations - GRADE 8 MATHEMATICS

To get/buy a soft copy, please send a request to queenyedda@gmail.com
Inclusions of the file attachment:
* Fonts used
* Soft copy of the WHOLE ppt slides with effects
* Complete activities
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Triangles (Similarity)

The document is an acknowledgement from a group of 5 students - Abhishek Mahto, Lakshya Kumar, Mohan Kumar, Ritik Kumar, and Vivek Singh of class X E. They are thanking their principal Dr. S.V. Sharma and math teacher Mrs. Shweta Bhati for their guidance and support in completing their project on triangles and similarity. They also thank their parents and group members for their advice and assistance during the project.

Slope of a Line

This document contains a lesson on slope of a line from a mathematics course. It includes examples of calculating slope given two points on a line, identifying whether graphs represent constant or variable rates of change, and word problems applying slope to real-world contexts like cost of fruit and gas. The key points are that slope is defined as the ratio of rise over run, or change in y over change in x, and represents the constant rate of change for linear equations and functions.

Polynomials

This document provides an overview of polynomials, including:
- Defining polynomials as expressions involving variables and coefficients using addition, subtraction, multiplication, and exponents.
- Discussing the history of polynomial notation pioneered by Descartes.
- Explaining the different types of polynomials like monomials, binomials, and trinomials.
- Outlining common uses of polynomials in mathematics, science, and other fields.
- Describing how to find the degree of a polynomial and graph polynomial functions.
- Explaining arithmetic operations like addition, subtraction, and division that can be performed on polynomials.

Simple Equations I

This document discusses solving one-step linear equations using addition and subtraction. It defines key terms like equations, solutions, and isolating variables. It explains that when transforming equations, the same operations must be applied to both sides to maintain equivalence. Inverse operations like addition and subtraction can isolate variables. Examples show how to isolate variables using addition or subtraction and solve equations. Students are then prompted to solve practice equations on their own. The document also discusses using equations to solve real-world problems, like finding a person's maximum heart rate based on their age.

Slope

The document discusses slope and how to calculate it. It defines slope as the rate of change of a line and provides the formula slope=rise/run. It then explains how to find the slope of a line graph by picking two points and calculating rise over run. Finally, it demonstrates how to find the slope of a line given two points or from a table of x-y values using the same rise over run formula.

Coordinate geometry

Coordinate geometry

Linear equations in two variables

Linear equations in two variables

Algebraic expressions

Algebraic expressions

11.2 graphing linear equations in two variables

11.2 graphing linear equations in two variables

Algebraic expressions and identities

Algebraic expressions and identities

Real numbers- class 10 mathematics

Real numbers- class 10 mathematics

Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring

Completing the square

Completing the square

Maths ppt linear equations in two variables

Maths ppt linear equations in two variables

PPT 7th grade math

PPT 7th grade math

Quadratic Formula Presentation

Quadratic Formula Presentation

MATHS - Linear equation in two variable (Class - X) Maharashtra Board

MATHS - Linear equation in two variable (Class - X) Maharashtra Board

Class IX Linear Equations in Two Variables

Class IX Linear Equations in Two Variables

Graphing linear equations

Graphing linear equations

Solving Linear Equations - GRADE 8 MATHEMATICS

Solving Linear Equations - GRADE 8 MATHEMATICS

Triangles (Similarity)

Triangles (Similarity)

Slope of a Line

Slope of a Line

Polynomials

Polynomials

Simple Equations I

Simple Equations I

Slope

Slope

Linear equations in two variables

Linear equations in two variables based on class 10th maths cbse
you can follow me on my insta manas.more12 for more ppts

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.

Linear equation in two variable

The document discusses methods for solving systems of linear equations in two variables:
1) Graphical method involves plotting the lines defined by each equation on a graph and finding their point of intersection.
2) Algebraic methods include substitution, elimination by equating coefficients, and cross-multiplication. Elimination involves manipulating the equations to eliminate one variable and solve for the other.
3) Examples demonstrate solving a system using substitution and elimination to find the solution values for x and y.

Linear equations

The document discusses various methods for solving systems of simultaneous linear equations with two variables. It explains that a system contains two or more linear equations involving the same variables. Common methods covered include substitution, where one variable is solved for and substituted into the other equation, and elimination, where coefficients are multiplied and equations are combined to eliminate one variable. Examples are provided to demonstrate both methods step-by-step. It emphasizes that solutions found must satisfy both original equations.

Pair of linear equations in two variable

Order of presentation
Anushka - Opening
Nikunj -Intro
Shubham - Graphical
Amel - Sunstitution
Siddhartha- Elimination
Karthik - Cross multiplication
Anushka - Equations reducible...& wrap-up
In case of any confusion..inform me by facebook, phone or in school

Module 1 plane coordinate geometry

The document provides information about module 1 on plane coordinate geometry. It will explain the relationship between lines on a plane, including intersecting, parallel and perpendicular lines. It will also cover determining the point of intersection between two lines algebraically and identifying if lines are parallel, perpendicular or neither based on their equations. Examples are provided to find the intersection of lines and to determine if lines are parallel, perpendicular or intersecting without graphing.

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.

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.

Lecture 11 systems of nonlinear equations

The document discusses solving systems of nonlinear equations in two variables. It provides examples of nonlinear systems that contain equations that are not in the form Ax + By = C, such as x^2 = 2y + 10. Methods for solving nonlinear systems include substitution and addition. The substitution method involves solving one equation for one variable and substituting into the other equation. The addition method involves rewriting the equations and adding them to eliminate variables. Examples demonstrate both methods and finding the solution set that satisfies both equations.

linearequns-classx-180912070018.pdf

This document discusses linear equations in two variables. It begins by presenting the general form of a linear equation as ax + by + c = 0, where a, b, and c are real numbers. It then explains that a single linear equation represents a straight line and can have infinitely many solution pairs (x,y). The document also discusses how two linear equations can have a unique solution if their lines intersect, no solution if the lines are parallel, or infinitely many solutions if the lines are coincident. Finally, it presents different algebraic methods for solving systems of two linear equations, including substitution, elimination of coefficients, and cross-multiplication.

CLASS X MATHS LINEAR EQUATIONS

This document discusses linear equations in two variables. It begins by presenting the general form of a linear equation as ax + by + c = 0, where a, b, and c are real numbers. It then explains that a linear equation can have infinitely many solutions (x,y value pairs) that satisfy the equation, and these solutions lie on a straight line. The document provides an example of a single linear equation and shows its graph on the Cartesian plane. It also discusses systems of two linear equations, explaining that their solutions occur where the lines intersect. The document covers various algebraic methods for solving systems of linear equations, including elimination by substitution or equating coefficients, and solving by cross multiplication. It provides examples to illustrate these solution

Ultimate guide to systems of equations

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.

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.

Pair of linear equation in two variables

it has all the discription about the easy chapter pair of linear equation in two variables. and if you like it so pleras

PAIR OF LINEAR EQUATION IN TWO VARIABLE

Power Point Presentation on a PAIR OF LINEAR EQUATION IN TWO VARIABLES, MATHS project...
Friends if you found this helpful please click the like button. and share it :) thanks for watching

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.

Pair Of Linear Equations In Two Variables

PowerPoint Presentation of Learning Outcomes, Experiential content, Explanation Content, Hot Spot, Curiosity Questions, Mind Map, Question Bank of
Pair Of Linear Equations In Two Variables Class X

Linear equation in two variables

This document discusses solving systems of linear equations in two variables. There are three main algebraic methods discussed: 1) elimination by substitution, which involves substituting one variable's expression into the other equation to get an equation with just one variable; 2) elimination by equating coefficients, which involves multiplying equations by constants and subtracting to eliminate one variable; and 3) cross-multiplication, which uses cross-multiplication of fractions to eliminate one variable. An example of using elimination by substitution to solve the system x + 2y = -1 and 2x - 3y = 12 is shown.

Mathematics ppt.pptx

1) The document provides information about linear equations in two variables including the general form of a linear equation, single linear equations, systems of two linear equations, conditions for common solutions, and methods to solve systems of linear equations algebraically.
2) Examples are provided to illustrate graphing single linear equations, finding common solutions to systems of two linear equations, and solving systems using elimination and cross-multiplication methods.
3) Key methods for solving systems of linear equations discussed include elimination by substitution or equating coefficients, and cross-multiplication. Conditions for common solutions depend on whether lines intersect, are parallel, or are coincident.

Pair of linear equations in two variables for classX

This document discusses methods for solving pairs of linear equations in two variables: substitution, elimination, and cross-multiplication. The substitution method involves solving one equation for one variable and substituting it into the other equation. The elimination method involves multiplying the equations by constants to make coefficients equal and then adding or subtracting the equations to eliminate one variable. The cross-multiplication method involves cross-multiplying the coefficients of the equations to derive an equation with one variable that can then be solved.

Linear equations in two variables

Linear equations in two variables

Linear equations Class 10 by aryan kathuria

Linear equations Class 10 by aryan kathuria

Linear equation in two variable

Linear equation in two variable

Linear equations

Linear equations

Pair of linear equations in two variable

Pair of linear equations in two variable

Module 1 plane coordinate geometry

Module 1 plane coordinate geometry

February 13, 2015

February 13, 2015

Maths

Maths

Lecture 11 systems of nonlinear equations

Lecture 11 systems of nonlinear equations

linearequns-classx-180912070018.pdf

linearequns-classx-180912070018.pdf

CLASS X MATHS LINEAR EQUATIONS

CLASS X MATHS LINEAR EQUATIONS

Ultimate guide to systems of equations

Ultimate guide to systems of equations

January18

January18

Pair of linear equation in two variables

Pair of linear equation in two variables

PAIR OF LINEAR EQUATION IN TWO VARIABLE

PAIR OF LINEAR EQUATION IN TWO VARIABLE

Analytic Geometry Period 1

Analytic Geometry Period 1

Pair Of Linear Equations In Two Variables

Pair Of Linear Equations In Two Variables

Linear equation in two variables

Linear equation in two variables

Mathematics ppt.pptx

Mathematics ppt.pptx

Pair of linear equations in two variables for classX

Pair of linear equations in two variables for classX

How to Manage Line Discount in Odoo 17 POS

This slide will cover the management of line discounts in Odoo 17 POS. Using the Line discount approach, we can apply discount for individual product lines.

Odoo 17 Events - Attendees List Scanning

Use the attendee list QR codes to register attendees quickly. Each attendee will have a QR code, which we can easily scan to register for an event. You will get the attendee list from the “Attendees” menu under “Reporting” menu.

Lecture_Notes_Unit4_Chapter_8_9_10_RDBMS for the students affiliated by alaga...

Title: Relational Database Management System Concepts(RDBMS)
Description:
Welcome to the comprehensive guide on Relational Database Management System (RDBMS) concepts, tailored for final year B.Sc. Computer Science students affiliated with Alagappa University. This document covers fundamental principles and advanced topics in RDBMS, offering a structured approach to understanding databases in the context of modern computing. PDF content is prepared from the text book Learn Oracle 8I by JOSE A RAMALHO.
Key Topics Covered:
Main Topic : DATA INTEGRITY, CREATING AND MAINTAINING A TABLE AND INDEX
Sub-Topic :
Data Integrity,Types of Integrity, Integrity Constraints, Primary Key, Foreign key, unique key, self referential integrity,
creating and maintain a table, Modifying a table, alter a table, Deleting a table
Create an Index, Alter Index, Drop Index, Function based index, obtaining information about index, Difference between ROWID and ROWNUM
Target Audience:
Final year B.Sc. Computer Science students at Alagappa University seeking a solid foundation in RDBMS principles for academic and practical applications.
About the Author:
Dr. S. Murugan is Associate Professor at Alagappa Government Arts College, Karaikudi. With 23 years of teaching experience in the field of Computer Science, Dr. S. Murugan has a passion for simplifying complex concepts in database management.
Disclaimer:
This document is intended for educational purposes only. The content presented here reflects the author’s understanding in the field of RDBMS as of 2024.
Feedback and Contact Information:
Your feedback is valuable! For any queries or suggestions, please contact muruganjit@agacollege.in

FINAL MATATAG Kindergarten CG 2023 pdf

FINAL MATATAG Kindergarten CG 2023.pdf

JavaScript Interview Questions PDF By ScholarHat

JavaScript Interview Questions PDF

What is Rescue Session in Odoo 17 POS - Odoo 17 Slides

In this slide, we will discuss the rescue session feature in Odoo 17 Point of Sale (POS). Odoo POS allows us to manage our sales both online and offline. The rescue session helps us recover data in case of internet connectivity issues or accidental session closure.

Introduction to Banking System in India.ppt

Bank – Banking – Banking System in India – Origin of Bank-Classification of Banks –Types of Customers RBI Functions- Commercial Banks – Functions

Parent PD Design for Professional Development .docx

Professional Development Papers

modul ajar kelas x bahasa inggris 2024-2025

modul ajar kelas x 2024-2025

DANH SÁCH THÍ SINH XÉT TUYỂN SỚM ĐỦ ĐIỀU KIỆN TRÚNG TUYỂN ĐẠI HỌC CHÍNH QUY N...

DANH SÁCH THÍ SINH XÉT TUYỂN SỚM ĐỦ ĐIỀU KIỆN TRÚNG TUYỂN ĐẠI HỌC CHÍNH QUY NĂM 2024
KHỐI NGÀNH NGOÀI SƯ PHẠM

formative Evaluation By Dr.Kshirsagar R.V

Formative Evaluation Cognitive skill

SEQUNCES Lecture_Notes_Unit4_chapter11_sequence

Title: Relational Database Management System Concepts(RDBMS)
Description:
Welcome to the comprehensive guide on Relational Database Management System (RDBMS) concepts, tailored for final year B.Sc. Computer Science students affiliated with Alagappa University. This document covers fundamental principles and advanced topics in RDBMS, offering a structured approach to understanding databases in the context of modern computing. PDF content is prepared from the text book Learn Oracle 8I by JOSE A RAMALHO.
Key Topics Covered:
Main Topic : DATA INTEGRITY, CREATING AND MAINTAINING A TABLE AND INDEX
Sub-Topic :
Data Integrity,Types of Integrity, Integrity Constraints, Primary Key, Foreign key, unique key, self referential integrity,
creating and maintain a table, Modifying a table, alter a table, Deleting a table
Create an Index, Alter Index, Drop Index, Function based index, obtaining information about index, Difference between ROWID and ROWNUM
Target Audience:
Final year B.Sc. Computer Science students at Alagappa University seeking a solid foundation in RDBMS principles for academic and practical applications.
About the Author:
Dr. S. Murugan is Associate Professor at Alagappa Government Arts College, Karaikudi. With 23 years of teaching experience in the field of Computer Science, Dr. S. Murugan has a passion for simplifying complex concepts in database management.
Disclaimer:
This document is intended for educational purposes only. The content presented here reflects the author’s understanding in the field of RDBMS as of 2024.

View Inheritance in Odoo 17 - Odoo 17 Slides

Odoo is a customizable ERP software. In odoo we can do different customizations on functionalities or appearance. There are different view types in odoo like form, tree, kanban and search. It is also possible to change an existing view in odoo; it is called view inheritance. This slide will show how to inherit an existing view in Odoo 17.

How To Update One2many Field From OnChange of Field in Odoo 17

There can be chances when we need to update a One2many field when we change the value of any other fields in the form view of a record. In Odoo, we can do this. Let’s go with an example.

Genetics Teaching Plan: Dr.Kshirsagar R.V.

A good teaching plan is a comprehensive write-up of the step-by-step and teaching methods helps students for understand the topic

CTD Punjab Police Past Papers MCQs PPSC PDF

CTD Punjab Police Past Papers MCQs PDF 2024

modul ajar kelas x bahasa inggris 24/254

modul ajar kelas x, 2024-2025

RDBMS Lecture Notes Unit4 chapter12 VIEW

Description:
Welcome to the comprehensive guide on Relational Database Management System (RDBMS) concepts, tailored for final year B.Sc. Computer Science students affiliated with Alagappa University. This document covers fundamental principles and advanced topics in RDBMS, offering a structured approach to understanding databases in the context of modern computing. PDF content is prepared from the text book Learn Oracle 8I by JOSE A RAMALHO.
Key Topics Covered:
Main Topic : VIEW
Sub-Topic :
View Definition, Advantages and disadvantages, View Creation Syntax, View creation based on single table, view creation based on multiple table, Deleting View and View the definition of view
Target Audience:
Final year B.Sc. Computer Science students at Alagappa University seeking a solid foundation in RDBMS principles for academic and practical applications.
Previous Slides Link:
1. Data Integrity, Index, TAble Creation and maintenance https://www.slideshare.net/slideshow/lecture_notes_unit4_chapter_8_9_10_rdbms-for-the-students-affiliated-by-alagappa-university/270123800
2. Sequences : https://www.slideshare.net/slideshow/sequnces-lecture_notes_unit4_chapter11_sequence/270134792
About the Author:
Dr. S. Murugan is Associate Professor at Alagappa Government Arts College, Karaikudi. With 23 years of teaching experience in the field of Computer Science, Dr. S. Murugan has a passion for simplifying complex concepts in database management.
Disclaimer:
This document is intended for educational purposes only. The content presented here reflects the author’s understanding in the field of RDBMS as of 2024.

How to Manage Early Receipt Printing in Odoo 17 POS

This slide will represent how to manage the early receipt printing option in Odoo 17 POS. Early receipts offer transparency and clarity for each customer regarding their individual order. Also printing receipts as orders are placed, we can potentially expedite the checkout process when the bill is settled.

Benchmarking Sustainability: Neurosciences and AI Tech Research in Macau - Ke...

In this talk we will review recent research work carried out at the University of Saint Joseph and its partners in Macao. The focus of this research is in application of Artificial Intelligence and neuro sensing technology in the development of new ways to engage with brands and consumers from a business and design perspective. In addition we will review how these technologies impact resilience and how the University benchmarks these results against global standards in Sustainable Development.

How to Manage Line Discount in Odoo 17 POS

How to Manage Line Discount in Odoo 17 POS

Odoo 17 Events - Attendees List Scanning

Odoo 17 Events - Attendees List Scanning

Lecture_Notes_Unit4_Chapter_8_9_10_RDBMS for the students affiliated by alaga...

Lecture_Notes_Unit4_Chapter_8_9_10_RDBMS for the students affiliated by alaga...

FINAL MATATAG Kindergarten CG 2023 pdf

FINAL MATATAG Kindergarten CG 2023 pdf

JavaScript Interview Questions PDF By ScholarHat

JavaScript Interview Questions PDF By ScholarHat

What is Rescue Session in Odoo 17 POS - Odoo 17 Slides

What is Rescue Session in Odoo 17 POS - Odoo 17 Slides

Introduction to Banking System in India.ppt

Introduction to Banking System in India.ppt

Parent PD Design for Professional Development .docx

Parent PD Design for Professional Development .docx

modul ajar kelas x bahasa inggris 2024-2025

modul ajar kelas x bahasa inggris 2024-2025

DANH SÁCH THÍ SINH XÉT TUYỂN SỚM ĐỦ ĐIỀU KIỆN TRÚNG TUYỂN ĐẠI HỌC CHÍNH QUY N...

DANH SÁCH THÍ SINH XÉT TUYỂN SỚM ĐỦ ĐIỀU KIỆN TRÚNG TUYỂN ĐẠI HỌC CHÍNH QUY N...

formative Evaluation By Dr.Kshirsagar R.V

formative Evaluation By Dr.Kshirsagar R.V

SEQUNCES Lecture_Notes_Unit4_chapter11_sequence

SEQUNCES Lecture_Notes_Unit4_chapter11_sequence

View Inheritance in Odoo 17 - Odoo 17 Slides

View Inheritance in Odoo 17 - Odoo 17 Slides

How To Update One2many Field From OnChange of Field in Odoo 17

How To Update One2many Field From OnChange of Field in Odoo 17

Genetics Teaching Plan: Dr.Kshirsagar R.V.

Genetics Teaching Plan: Dr.Kshirsagar R.V.

CTD Punjab Police Past Papers MCQs PPSC PDF

CTD Punjab Police Past Papers MCQs PPSC PDF

modul ajar kelas x bahasa inggris 24/254

modul ajar kelas x bahasa inggris 24/254

RDBMS Lecture Notes Unit4 chapter12 VIEW

RDBMS Lecture Notes Unit4 chapter12 VIEW

How to Manage Early Receipt Printing in Odoo 17 POS

How to Manage Early Receipt Printing in Odoo 17 POS

Benchmarking Sustainability: Neurosciences and AI Tech Research in Macau - Ke...

Benchmarking Sustainability: Neurosciences and AI Tech Research in Macau - Ke...

- 1. LINEAR EQUATIONS IN TWO VARIABLES BY: DR. VIVEK NAITHANI TGT MATHS KENDRIYA VIDYALAYA SANGATHAN Copyright Information: CC by SA 4.0
- 2. DEFINITION: An equation that contains two variables and the degree of each variable being 1 is called linear equation in two variables. e.g. : 2x+3y =7 3x- 6y =34 A system of linear equations always exists in pair of equations.
- 3. GENERAL LINEAR EQUATION IN TWO VARIABLES The general form of simultaneous linear equations is: a1x + b1y = c1 ------------------- (1) a2x + b2y = c2 -------------------- (2) Here a1, a2 are the co-efficients of x b1, b2 are the co-efficients of y c1, c2 are the constants. Note: Both a & b together are never 0
- 4. FRAMING A LINEAR EQUATION IN TWO VARIABLES To frame a linear equation in two variables working rule is: 1. Select the unknown and assign variables to the unknown. 2. Select the given condition and frame the variables in the given first and second conditions. 3. Frame the equations.
- 5. EXAMPLE: Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Represent this situation algebraically. Here two unknowns are age of Aftab and age of daughter. Let present age of Aftab be x and present age of daughter be y. I condition: 7 years ago Aftab was 7 times as old as his daughter 7 years ago age if Aftab = (x-7) and age of his daughter = (y-7) years ∴ (x-7) = 7 X (y-7) ⇒ x- 7 = 7y -49 ⇒ x – 7y = -42 x – 7y = -42 This is first equation in two variables.
- 6. II Condition: Three years from now, Aftab shall be three times as old as his daughter will be. After 3 years: Aftab’s age = x+3 Daughter’s age = y+3 ⇒ (x+3) = 3 X (y+3) ⇒ x+3 = 3y +9 ⇒ x -3y = 6 This is second linear equation Hence the set of linear equation in two variables is x – 7y = -42 ---------------(1) x -3y = 6 ---------------------(2)
- 7. GRAPHICAL REPRESENTATION OF SIMULATENOUS LINEAR EQUATIONS • A pair of simultaneous linear equation represents a pair of straight lines on a graph sheet.
- 8. CRITERIA OF CONSISTENCY OF SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS For a given set of pair of linear equations in two variables: a1x + b1y = c1 ------------------- (1) a2x + b2y = c2 -------------------- (2) The following cases arise as solution of the given set of equations: 1. CASE I: If 𝑎1 𝑎2 ≠ 𝑏1 𝑏2 then the system is consistent and has a unique solution.
- 10. Case II: If 𝒂𝟏 𝒂𝟐 = 𝒃𝟏 𝒃𝟐 ≠ 𝒄𝟏 𝒄𝟐 then the system is inconsistent and has no solution. The lines on the graph are parallel.
- 11. Case II: If 𝑎1 𝑎2 = 𝑏1 𝑏2 = 𝑐1 𝑐2 then the system is consistent and has infinitely many solutions. The lines on the graph are coincident.
- 12. ALGEBRAIC SOLUTION OF SIMULATNEOUS LINEAR EQUATIONS The following methods are being used to solve simultaneous linear equations algebraically: 1.Elimination Method. 2.Substitution Method. 3.Cross multiplication method.
- 13. ELIMINATION METHOD: In this method we eliminate one of the two variables to achieve the desired results Solve the equations 2x+y = 5 and 3x+2y =8. 2x+y = 5 --------(1) X 3 [ Here we multiply the equations with the suitable non-zero 3x+2y = 8 -------(II) X 2 constants to make co-efficients of the variable to be eliminated equal.] So our equations become 6x +3y = 15 {Here we are eliminating x and now 6x +4y = 16 subtracting the new equations we get} -y = -1 ⇒ y = 1 Substituting y =1 in any of the equations (Here we are substituting in eqn. 1) we get 2x +1= 5 ⇒ 2x = 4 ⇒ x= 2.
- 14. SUBSTITUTION METHOD: STEP 1: In this method we first choose an equation and then express any one of the two variables in terms of the other. STEP 2: Then we substitute the function obtained in step 1 in the another equation. STEP 3: Now we get an equation in a single variable which on solving will give value of one variable. STEP 4: The value obtained in step 3 will be substituted in the another equation to get the value of another variable.
- 15. EXAMPLE Solve the equations 2x+y = 5 and 3x+2y =8. 2x+y = 5 ⇒ y = 5- 2x { Here variable y has been expressed in terms of x} Substituting y = 5-2x in the second equation we get 3x + 2(5-2x) = 8 ⇒ 3x + 10 -4x = 8 ⇒ 3x-4x = 8-10 ⇒ -x = -2 ⇒ x = 2 Now substituting x= 2 in y = 5-2x we get y = 5 – 2(2) = 5-4 = 1 Hence the solution is x = 2 and y = 1.
- 16. CROSS MULTIPLICATION METHOD: The given equations are a1x+b1y + c1= 0 and a2x+b2y+c2= 0 a1x+b1y + c1= 0 a2x+b2y+c2 = 0 For solving this system of equation we follow a pattern given in following diagram
- 17. Hence we get the following result: Solving this first and third fractions we will get the value of x and solving second and third fractions we will get the value of y.
- 18. Solve the following equations x-3y-7=0 and 3x-3y-15=0 x-3y-7 = 0 3x-3y-15= 0 𝒙 −𝟑 𝑿 −𝟏𝟓 − −𝟑 𝑿(−𝟕) = 𝒚 𝟑 𝑿 −𝟕 − 𝟏 𝑿(−𝟏𝟓) = 𝟏 𝟏 𝑿 −𝟏𝟓 − 𝟑 𝑿(−𝟕) Which gives 𝑥 45 − 21 = 𝑦 −21 + 15 = 1 −15 + 21 𝑥 24 = 𝑦 −6 = 1 6 Solving fraction 1 and 3 we get x = 24/6 = 4 Solving fraction 2 and 3 we get y = -6/6 = -1. Hence Solution is x= 4 and y = -1