# NCERT Solutions for Class 10 Maths Chapter 3 : Pair Of Linear Equations In Two Variables

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## Chapter 3 : Pair Of Linear Equations In Two Variables

### 3.1 Introduction

You must have come across situations like the one given below :
Akhila went to a fair in her village. She wanted to enjoy rides on the Giant Wheel and play Hoopla (a game in which you throw a ring on the items kept in a stall, and if the ring covers any object completely, you get it).

### 3.2 Pair of Linear Equations in Two Variables

Recall, from Class IX, that the following are examples of linear equations in two variables:
You also know that an equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables x and y.

### 3.3 Graphical Method of Solution of a Pair of Linear Equations

In the previous section, you have seen how we can graphically represent a pair of linear equations as two lines.
You have also seen that the lines may intersect, or may be parallel, or may coincide.
Can we solve them in each case? And if so, how?
We shall try and answer these questions from the geometrical point of view in this section.

### 3.4 Algebraic Methods of Solving a Pair of Linear Equations

In the previous section, we discussed how to solve a pair of linear equations graphically. The graphical method is not convenient in cases when the point representing the solution of the linear equations has non-integral coordinates like.
There is every possibility of making mistakes while reading such coordinates.
Is there any alternative method of finding the solution?
There are several algebraic methods, which we shall now discuss.

### 3.4.1 Substitution Method :

We shall explain the method of substitution by taking some examples.

### 3.4.2 Elimination Method

Now let us consider another method of eliminating (i.e., removing) one variable.
This is sometimes more convenient than the substitution method.
Let us see how this method works.

### 3.4.3 Cross - Multiplication Method

So far, you have learnt how to solve a pair of linear equations in two variables by graphical, substitution and elimination methods.
Here, we introduce one more algebraic method to solve a pair of linear equations which for many reasons is a very useful method of solving these equations.
Before we proceed further, let us consider the following situation.

### 3.5 Equations Reducible to a Pair of Linear Equations in Two Variables

In this section, we shall discuss the solution of such pairs of equations which are not linear but can be reduced to linear form by making some suitable substitutions.
We now explain this process through some examples.

### 3.6 Summary

In this chapter, you have studied the following points:
1. Two linear equations in the same two variables are called a pair of linear equations in two variables.
2. A pair of linear equations in two variables can be represented, and solved, by the:

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