# NCERT Exemplar Class 10 Maths Chapter 3 Solutions: Pair of Linear Equations in Two Variables

NCERT Exemplar Class 10 Maths Solutions for Chapter 3 will help you practice the concepts of the chapter better for your CBSE exams. In this chapter of NCERT Class 10 Maths Exemplar, you will be introduced to the linear equations in two variables and different graphical and algebraic methods of finding the solutions of a given pair of equations. Also, you will get to practice converting different kinds of equations into a pair of linear equations in two variables and solve them easily.

There are 54 questions in total given in the 4 NCERT Exemplar exercises covering the topics of the chapter thoroughly. You will learn excellent time management skills by practising the diverse set of exercises of the chapter. The difficulty level of the questions will increase as you will proceed in the exercises, thus helping you to brush up for challenging problems. The questions in the NCERT Exemplar Class 10 Maths Chapter 3 are both objective and subjective in nature.

The maths faculty at Instasolv has created the answers in a student-friendly language. You will find it very reliable to use Instasolv’s answer as the source of reference whenever you stumble upon doubts in this chapter. The NCERT Exemplar solutions by Instasolv will also aid you in completing homework in lesser time with more clarity on this topic of your CBSE Class 10 Maths syllabus.

## Important Topics in the NCERT Exemplar Class 10 Maths Solutions Chapter 3

**Introduction**

If we have a system of the equation that comprises of 2 linear equations and have the same two variables then we term it as a pair of linear equations in two variables.

It is represented as

a_{1}x+b_{1}y+c_{1}=0

a_{2}x+b_{2}y+c_{2}=0

such that a_{1}, a_{2}, b_{1}, b_{2}, c_{1}, c_{2 }are real numbers and a_{1}^{2}+b_{1}^{2}≠0, a_{2}^{2}+b_{2}^{2}≠0

**Graphical Method**

There are 2 lines in the graph of such a pair of linear equations.

- If these lines intersect at one point, there is the existence of a unique solution for these equations, and they are termed as consistent solutions.
- If these lines are coincident over one another, there are infinite solutions to these equations and this system of equations are termed as a dependent term.
- If the two lines in the graph are parallel to one another, then there are no solutions and it is known as an inconsistent pair.

**Algebraic Methods:**

To find the solutions of the pair of linear equations in two variables, we can employ the following methods:

- Substitution method
- Elimination method
- Cross-multiplication method.

We can also find the consistency of the pair of linear equations by algebraic expression in the following manner:

If we consider a pair of linear equations in 2 variables such that,

a_{1}x+b_{1}x+c_{1}=0

a_{2}x+b_{2}x+c_{2}=0

Then when a_{1}/a_{2 }≠ b_{1}/b_{2}, the pair is consistent.

When a_{1}/a_{2 }= b_{1}/b_{2 }≠ c_{1}/c_{2, }the pair is inconsistent.

When a_{1}/a_{2 }= b_{1}/b_{2 }= c_{1}/c_{2}, the pair is dependent and consistent.

### Exercise Discussion of the NCERT Exemplar Class 10 Maths Chapter 3

- The first exercise 3.1 is a set of multiple-choice questions based on the graphical solutions of the pair of linear equations and the type of solutions of linear equations.
- Exercise 3.2 of this chapter in NCERT Exemplar Class 10 Maths is more of a conceptual exercise that will help you in identifying the consistency of equations based on the reasoning in line with the graphs of the equations.
- Exercise 3.3 is a comprehensive set of questions of short answer type in which you have to find the coefficients of linear equations so that they have no solution, infinite solutions and unique solution.
- Lastly, in exercise 3.4, you will get to solve a wide variety of graphical questions and word problems that will employ the graphical method, substitution, elimination and the cross multiplication methods for solving a pair of linear equations of 2 variables.
- By solving these questions, you will get an idea of the pattern of questions in the exam.

### Why use NCERT Exemplar Class 10 Maths Solutions Chapter 3 by Instasolv?

- We have solved all NCERT Exemplar problems for Class 10 Maths Chapter 3 in order to provide you detailed answers to all the queries related to this chapter.
- These answers at Instasolv are provided to you absolutely free of cost.
- We have written the answers in such a fashion that these are ideal for self-study.
- Each and every question have been answered in a step by step format at Instasolv.