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3. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Exploration of pair of linear equations in two variables offers insights into graphical and algebraic methods for finding solutions. Key concepts include identifying consistent, inconsistent, and dependent systems of equations while analyzing their graphical representations. Various mathematical representations and methods to approach these equations are emphasized throughout the chapter.

Sections

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

This section covers the representation and solution of pairs of linear equations in two variables using graphical and algebraic methods.

3 Section Overview

Start current section content and materials

3.1 Introduction

This section introduces the concept of pair of linear equations in two variables through relatable examples and outlines the methods to represent and solve these equations.

3.2 Graphical Method of Solution of a Pair of Linear Equations

This section introduces the graphical method for solving pairs of linear equations in two variables, detailing conditions for consistent, inconsistent, and dependent equations.

3.3 Algebraic Methods of Solving a Pair of Linear Equations

This section explores algebraic methods for solving pairs of linear equations, focusing on substitution and elimination methods.

3.3.1 Substitution Method

The Substitution Method is an effective algebraic technique used to solve pairs of linear equations by expressing one variable in terms of the other and substituting it into the other equation.

3.3.2 Elimination Method

The elimination method is a systematic approach to solving pairs of linear equations by removing one variable to simplify the equations.

3.4 Summary

This section provides a concise overview of various methods to solve a pair of linear equations in two variables, including graphical and algebraic approaches.

Learning Objectives

  • Understanding the representation of pairs of linear equations in two variables.

  • Applying graphical and algebraic methods to solve linear equations.

  • Identifying the nature of solutions based on the intersection of lines.

Key Concepts

Consistent Pair of Linear Equations

A pair of linear equations that has at least one solution. Graphically, represented by two intersecting lines.

Inconsistent Pair of Linear Equations

A pair of linear equations that do not have any solutions, represented by parallel lines.

Dependent Pair of Linear Equations

A pair of linear equations that has infinitely many solutions, represented by coincident lines.

Graphical Method

A method of solving linear equations by plotting their graphs and identifying points of intersection.

Algebraic Methods

Techniques like substitution and elimination used to solve pairs of linear equations by manipulating the equations algebraically.

Practice Exercises

Total Questions

3

Estimated Time

6 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting