Pair of Linear Equations in Two Variables

Introduction

Can we find the solutions of this pair of equations? There are several ways of finding these, which we will study in this chapter.Recall, that you have studied in Class IX that the geometrical (i.e., graphical) representation of a linear equation in two variables is a straight line. Can you now suggest what a pair of linear equations in two variables will look like, geometrically? There will be two straight lines, both to be considered together.

You have also studied in Class IX that given two lines in a plane, only one of the following three possibilities can happen:

1. The two lines will intersect at one point.

2. The two lines will not intersect, i.e., they are parallel.

3. The two lines will be coincident.

Graphical Method of Solution of a Pair of Linear Equations, Substitution Method, Elimination Method, Cross - Multiplication Method, Equations Reducible to a Pair of Linear Equations in Two Variables, Algebraic Methods of Solving a Pair of Linear Equations, Elimination Method, Cross - Multiplication Method are different methods of solving linear equations in two variables.