NCERT Class 10 Maths Exercise 3.2 Solutions | Pair of Linear Equations

Short Introduction

Exercise 3.2 of NCERT Class 10 Maths Chapter 3 focuses on solving a pair of linear equations using the Substitution Method. This exercise includes direct equations as well as word problems based on ages, angles, fractions, and real-life situations.

These solutions are prepared in a simple, step-by-step manner to help students understand the concepts clearly and score better in examinations.

Quick Information Box

Particular Details
Class 10
Subject Mathematics
Chapter Pair of Linear Equations in Two Variables
Exercise 3.2
Method Used Substitution Method
Board CBSE & State Boards
Difficulty Level Moderate

Concepts Used (Topics Covered)

✔ Pair of Linear Equations in Two Variables

✔ Substitution Method

✔ Solving Real-Life Word Problems

✔ Verification of Solutions

✔ Forming Equations from Statements

✔ Application of Linear Equations

Important Formulas

General Form of a Linear Equation

ax + by + c = 0

Steps of Substitution Method

  1. Express one variable in terms of another.
  2. Substitute it into the second equation.
  3. Solve the resulting equation.
  4. Substitute back to find the second variable.
  5. Verify the answer.

Question 1 Solve the following pair of linear equations by the substitution method.

(i)

x + y = 14

x − y = 4

Solution

Question 1 (ii)

Solve:

s − t = 3

s/3 + t/2 = 6

Solution

Question 1 (iii)

Solve:

3x − y = 3

9x − 3y = 9

Solution

Question 1 (iv)

Solve:

0.2x + 0.3y = 1.3

0.4x + 0.5y = 2.3

Solution

Question 1 (v)

Solve:

√2x + √3y = 0

√3x − √8y = 0

Question 1 (vi)

Solve:

3x/2 − 5y/3 = −2

x/3 + y/2 = 13/6

Question 2 Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.

Solve:

2x + 3y = 11

2x − 4y = −24

Solution

Question 3 Form the pair of linear equations for the following problems and find their solution by
substitution method.

(i)

Solution

Question 3 (ii)

The larger of two supplementary angles exceeds the smaller by 18 degrees. Find
them.

Question 3 (iii)

The coach of a cricket team buys 7 bats and 6 balls for ₹3800. Later, she buys 3 bats and 5 balls for ₹1750. Find the cost of each bat and each ball.

Question 3 (iv)

The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹105 and for a journey of 15 km, the charge paid is ₹155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

Question 3 (v)

(v) A fraction becomes 9/11, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction.

Question 3 (vi)

Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

Common Mistakes

❌ Sign errors during substitution.

❌ Incorrect formation of equations.

❌ Forgetting to verify the answer.

❌ Errors in simplifying fractions.

Exam Tips

✅ Write equations clearly.

✅ Use substitution carefully.

✅ Verify the final answer.

✅ Mention units wherever required.

✅ Practice word problems regularly.

Practice MCQs

1. The solution of x + y = 8 and x − y = 2 is:

A. (5,3)

B. (3,5)

C. (4,4)

D. (6,2)

Answer: A

2. Coincident lines have:

A. One solution

B. No solution

C. Infinitely many solutions

D. Two solutions

Answer: C

3. In substitution method, the first step is:

A. Draw the graph

B. Eliminate variables

C. Express one variable in terms of another

D. Add equations

Answer: C

Frequently Asked Questions (FAQs)

Q1. Which method is used in Exercise 3.2?

The Substitution Method.

Q2. Are these questions important for board exams?

Yes, they are frequently asked.

Q3. Are word problems important?

Yes, they carry good marks in examinations.

Q4. How many marks can be expected from this chapter?

Generally, 4–6 marks.

Conclusion

Exercise 3.2 helps students understand how to solve a pair of linear equations algebraically using the substitution method. Regular practice of these questions improves problem-solving skills and builds a strong foundation for higher mathematics.

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