## CBSE NCERT Solutions for Chapter 3 Pair of Linear Equation in two Variables Class 10 Maths

We have learnt about Linear equations in previous classes.  In previous chapter we have also learnt about linear polynomials. Linear polynomial when equated with zero results in linear equation. A linear equation having two variables can have infinite number of pair of solutions.  On XY plane the linear equation in two variables is represented by a straight line. Every coordinate on the line is the solution of the given equation.  There are three types of system of Linear Equation. In the first type of system, there are infinite numbers of solutions of the system. On XY plane, graph of both equations coincides each other.  In second type, the graph of both equations cut at one point. In this case, there is unique solution of this system of equation. The coordinate points at which graph cuts each other is the solution of the equation.  Both type of system is known as consistent solution.  The last case when graph of both equation never meets, that means, there is no solution to the system of linear equation.  Algebraic condition to check the type of system of pair of linear equation in two variables has also been mentioned. Questions are asked on these conditions which are related to coefficients of both equations. Graphical method to solve linear equation is discussed. After that three Algebraic methods to solve pair of linear equations in two variables is discussed.  They are substitution method, elimination method and cross multiplication method.  Word problems are asked based on real life situations. The given situation is represented in form of pair of linear equation in two variables. Some types of problem asked are regarding numerator-denominator of a fraction. Other examples are river-boat  problem, age based problems and other miscellaneous questions.  Total of 4 exercises has been given to understand different systems, solve linear equations using different methods, and solve word problems.