NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

The Maths Chapter 3 Pair of Linear Equations in two variables deals with Linear equations, pair of linear equations, and different methods to solve it. A linear equation of two variables x and y is defined as an equation of the form "ax+by+c=0" where a and b are non-zero integers. It is clear that every solution of the equation is a point on the respective line representing it. The pair of linear equations in two variables is considered when two equations have the same set of variables.

It can be solved using the Graphical method by plotting the lines on the graph and finding the interesting point. It can also be concluded that if the lines intersect, there is exactly one solution. When they coincide, there are infinite solutions, and when they are parallel, there are no solutions which also can be verified using the coefficients of both the equation.

The NCERT Maths Chapter 3 Pair of Linear Equations in two variables comprises Algebraic methods like Substitution Method, Elimination Method, Cross - Multiplication Method, to find out the solution. Substitution and Elimination require less calculation and considered as easiest way to solve pair of linear equations. In the case of the elimination method, one variable is eliminated first to get a linear equation in one variable. Multiply either of the equation with an integer to get two relevant equations and solve it by using either of the operations like addition or subtraction.

In few cases, equations that are not linear can be converted to linear equations by making few required substitutions.

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