CBSE Class 8 Maths Chapter 2: Linear Equations in One Variable NCERT Solutions

Reviewed by NCERT Help Editorial Team · Updated on 29 Jul 2026

NCERT Solutions PDF Class 8 PDF

CBSE Class 8 Mathematics Chapter 2, Linear Equations in One Variable, introduces students to the core concepts of algebraic equations with a single variable. This chapter breaks down the process of solving these equations into manageable steps, utilizing fundamental algebraic operations like addition, subtraction, multiplication, and division to isolate the unknown variable. The NCERT Solutions offer detailed, step-by-step explanations for all exercises, ensuring clarity and reinforcing understanding. By working through these solutions, students can develop a robust grasp of algebraic manipulation and build confidence in tackling various problems. This resource is an excellent tool for exam preparation, aiming to equip students with the skills needed to solve linear equations accurately and efficiently, laying a strong groundwork for future mathematical studies.

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Quick info

Board	CBSE
Class	Class 8
Subject	Mathematics
Session	2026
Language	English
Type	NCERT Solutions
Chapter	Chapter 2

Chapter summary

Chapter 2 of the Class 8 NCERT Mathematics textbook deals with Linear Equations in One Variable. This section provides detailed, step-by-step solutions for the exercises, focusing on the basic principles of solving equations. It covers techniques for finding the value of an unknown variable in equations with a single variable, using inverse operations to isolate the variable. The solutions aim to reinforce understanding of algebraic manipulation.

Learning outcomes

Understand the concept of a linear equation in one variable.
Learn to solve linear equations using basic arithmetic operations.
Apply the principle of balancing equations by performing the same operation on both sides.
Isolate the variable to find its value.
Solve equations involving fractions.
Solve equations involving multiplication and division.

Topics covered

Paper topics

Linear Equations in One Variable
Solving Equations by Addition
Solving Equations by Subtraction
Solving Equations by Multiplication
Solving Equations by Division
Equations with Fractional Coefficients
Algebraic Manipulation

Important topics

Introduction to Linear Equations
Solving Basic Linear Equations
Equations involving Fractions
Isolating the Variable

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Questions and Solutions

Question 1

Solve the following equation: $x-2=7$

Solution:

To solve the equation $x-2=7$ , we need to isolate the variable $x$ . We can do this by adding 2 to both sides of the equation to cancel out the -2 on the left side.

$x - 2 + 2 = 7 + 2$

This simplifies to:

$x = 9$

Thus, the solution is $x=9$ .

Question 2

Solve the following equation: $y + 3 = 10$

Solution:

In the equation $y + 3 = 10$ , we want to find the value of $y$ . To isolate $y$ , we subtract 3 from both sides of the equation.

$y + 3 - 3 = 10 - 3$

Performing the subtraction gives:

$y = 7$

The value of $y$ is 7.

Question 3

Solve the following equation: $6 = z + 2$

Solution:

We are given the equation $6 = z + 2$ . To find the value of $z$ , we need to get $z$ by itself. We can achieve this by subtracting 2 from both sides of the equation.

$6 - 2 = z + 2 - 2$

This calculation results in:

$4 = z$

Therefore, $z = 4$ .

Question 4

Solve the following equation: $\frac{3}{7} + x = \frac{17}{7}$

Solution:

To solve the equation $\frac{3}{7} + x = \frac{17}{7}$ for $x$ , we need to eliminate the fraction $\frac{3}{7}$ from the left side. We do this by subtracting $\frac{3}{7}$ from both sides of the equation.

$x + \frac{3}{7} - \frac{3}{7} = \frac{17}{7} - \frac{3}{7}$

This simplifies the equation to:

$x = \frac{17 - 3}{7}$

Performing the subtraction in the numerator:

$x = \frac{14}{7}$

Finally, we simplify the fraction:

$x = 2$

The solution is $x=2$ .

Question 5

Solve the following equation: $6x = 12$

Solution:

Given the equation $6x = 12$ , our goal is to find the value of $x$ . Since $x$ is multiplied by 6, we perform the inverse operation, which is division. We divide both sides of the equation by 6.

$\frac{6x}{6} = \frac{12}{6}$

This simplifies to:

$x = 2$

Therefore, the solution is $x=2$ .

Question 6

Solve the following equation: $\frac{t}{5} = 10$

Solution:

In the equation $\frac{t}{5} = 10$ , the variable $t$ is divided by 5. To isolate $t$ , we perform the inverse operation, which is multiplication. We multiply both sides of the equation by 5.

$\frac{t}{5} \times 5 = 10 \times 5$

This calculation yields:

$t = 50$

The solution to the equation is $t=50$ .

Common mistakes

Errors in applying inverse operations (e.g., adding instead of subtracting).
Incorrectly handling fractions when solving equations.
Arithmetic mistakes during calculation.
Confusing the variable's coefficient with the variable itself.

Revision tips

Review the basic properties of equality before starting.
Practice each type of operation (addition, subtraction, multiplication, division) separately.
Check your answers by substituting the found value back into the original equation.
Pay close attention to signs when moving terms across the equals sign.

Practice MCQs

Q1. What is the value of x in the equation x - 2 = 7?

Q2. If y + 3 = 10, what is the value of y?

Q3. Solve for z in the equation 6 = z + 2.

Q4. What is the solution for x in the equation $ $\frac{3}{7}$ + $x = \frac{17}$ {7}$?

Q5. Find the value of x if 6x = 12.

Q6. Solve for t in the equation $ $\frac{t}{5}$ = 10$.

Frequently asked questions

What is a linear equation in one variable?

A linear equation in one variable is an equation that can be written in the form ax + b = 0, where 'a' and 'b' are constants and 'a' is not equal to zero, and it contains only one variable (like x, y, or t).

How do you solve a linear equation?

To solve a linear equation, you use inverse operations to isolate the variable on one side of the equation. Whatever operation you perform on one side, you must perform the same operation on the other side to maintain equality.

What are the basic operations used to solve linear equations?

The basic operations are addition, subtraction, multiplication, and division. These are used to undo the operations applied to the variable.

How can I check if my solution is correct?

Substitute the value you found for the variable back into the original equation. If both sides of the equation are equal, your solution is correct.

Are these solutions suitable for exam revision?

Yes, these NCERT solutions provide clear, step-by-step explanations that are excellent for revising the concepts and practicing problem-solving techniques for exams.

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CBSE Class 8 Maths Chapter 2: Linear Equations in One Variable NCERT Solutions

Quick info

Chapter summary

Learning outcomes

Topics covered

Paper topics

Important topics

PDF preview

Questions and Solutions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Common mistakes

Revision tips

Practice MCQs

Frequently asked questions

Important links