Class 9 NCERT Solutions Chapter 4 Linear Equations in two variables Exercise 4.1 (original) (raw)

Last Updated : 23 Jul, 2025

Chapter 4 of the Class 9 NCERT Mathematics textbook, titled "Linear Equations in Two Variables," introduces students to the concept of linear equations involving two variables. This chapter explains how to represent linear equations graphically and how to interpret the solutions. Exercise 4.1 focuses on the basic understanding of linear equations, including the formulation of equations and their graphical representation.

NCERT Solutions for Class 9 - Chapter 4 Linear Equations in Two Variables - Exercise 4.1

This section provides detailed solutions for Exercise 4.1 from Chapter 4 of the Class 9 NCERT Mathematics textbook. The exercise includes problems that help students understand how to write linear equations in two variables, identify solutions, and represent them graphically on a coordinate plane. The solutions are explained step-by-step to aid students in grasping these fundamental concepts.

In this article, we will be going to solve the entire exercise 4.1 of our NCERT textbook. Linear equations are the parts of algebra in which we see a lot of equations and we solve them to get a proper value.

What are Linear Equations?

A linear equation is an equation that forms a straight line when graphed on a coordinate plane. It is typically written in the form ax+by=c, where a, b, and c are constants, and x and y are variables. In its simplest form, a linear equation in one variable can be written as ax+b=0.

For example:

**Question 1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

**Solution:

Let's take the cost of a notebook as Rs. x and the cost of a pen as Rs. y.

Given that cost of a notebook (x) is twice the cost of a pen(y).

So, x = 2y.

x - 2y = 0

x - 2y = 0 is the linear equation in two variables that represent the statement.

**Question 2. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:

****(i) 2x + 3y = 9.35**

**Solution:

2x + 3y - 9.35 = 0 (Transposing 9.35 to LHS)

(2)x + (3)y + (-9.35) = 0 (converting it in the form ax + by + c = 0)

On comparing equation with ax + by + c = 0,

We get **a = 2, b = 3, c = -9.35

****(ii) x - y/5 -10 = 0**

**Solution:

(5x - y - 50)/5 = 0 (Multiply and divide the whole equation by 5)

5x - y - 50 = 0

(5)x + (-1)y + (-50) = 0 (converting it in the form ax + by + c = 0)

On comparing equation with ax + by +c =0,

We get **a = 5, b = -1, c = -50

****(iii) -2x + 3y = 6**

**Solution:

-2x + 3y - 6 = 0 (Transposing 6 to LHS)

(-2)x + (3)y+ (-6) = 0 (converting it in the form ax + by + c = 0)

On comparing equation with ax + by +c =0,

We get a = -2, b = 3, c = -6

****(iv) x = 3y**

**Solution:

x - 3y = 0 (Transposing 3y to LHS)

(1)x + (-3)y + 0 = 0 (converting it in the form ax + by + c = 0)

On comparing equation with ax + by + c = 0,

We get **a = 1, b = -3, c = 0

****(v) 2x = -5y**

**Solution:

2x + 5y = 0 (Transposing 5y to LHS)

(2)x + (5)y + 0 = 0 (converting it in the form ax + by + c = 0)

On comparing equation with ax + by +c =0,

We get **a = 2, b = 5, c = 0

****(vi) x + 2 = 0**

**Solution:

(1)x + (0)y + 2 = 0 (converting it in the form ax + by + c = 0)

On comparing equation with ax + by +c =0,

We get **a = 1, b = 0, c = 2

****(vii) y - 2 = 0**

**Solution:

(0)x + (1)y + (-2) = 0 (converting it in the form ax + by + c = 0)

On comparing equation with ax + by +c =0,

We get a = 0, b = 1, c = -2

****(viii) 5 = 2x**

**Solution:

5 - 2x = 0 (Transposing 2x to LHS)

(-2)x + (0)y + 5 = 0 (converting it in the form ax + by + c = 0)

On comparing equation with ax + by + c = 0,

We get **a = -2, b = 0, c = 5

Summary

Chapter 4 of the Class 9 NCERT Mathematics textbook, "Linear Equations in Two Variables," introduces the concept of linear equations involving two variables. Exercise 4.1 focuses on helping students understand how to write and graph linear equations, identify solutions, and check whether a given point is a solution. The exercise emphasizes the graphical representation of these equations, demonstrating that the graph of a linear equation is a straight line and that such equations have infinitely many solutions.