Short Introduction

Exercise 3.3 of NCERT Class 10 Maths Chapter 3 focuses on solving a pair of linear equations in two variables using the Elimination Method and Substitution Method. This exercise also includes real-life word problems involving ages, fractions, numbers, money, and library charges.

---

Quick Information Box

Particular	Details
Class	10
Subject	Mathematics
Chapter	Pair of Linear Equations in Two Variables
Exercise	3.3
Methods Used	Elimination Method and Substitution Method
Difficulty Level	Easy to Moderate

---

Concepts Used (Topics Covered)

✔ Pair of Linear Equations in Two Variables

✔ Elimination Method

✔ Substitution Method

✔ Formation of Equations

✔ Age Problems

✔ Digit Problems

✔ Money Problems

✔ Word Problems

---

Important Formulas

General Form of Linear Equation

ax + by + c = 0

Unique Solution

a₁/a₂ ≠ b₁/b₂

No Solution

a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Infinitely Many Solutions

a₁/a₂ = b₁/b₂ = c₁/c₂

---

Question 1 Solve the following pair of linear equations by the elimination method and the substitution
method :

(i)

x + y = 5

2x – 3y = 4

---

Question 1 (ii)

3x + 4y = 10

2x − 2y = 2

---

Question 1 (iii)

3x − 5y = 4

9x − 2y = 7

---

Question 1 (iv)

x/2 + 2y/3 = −1

x − y/3 = 3

---

Question 2 (i)

If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2
if we only add 1 to the denominator. What is the fraction?

---

Question 2 (ii)

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

---

Question 2 (iii)

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

---

Question 2 (iv)

Meena went to a bank to withdraw ₹2000. She asked the cashier to give her ₹50 and ₹100 notes only. Meena got 25 notes in all. Find how many notes of ₹50 and ₹100 she received.

---

Question 2 (v)

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹27 for a book kept for seven days, while Susy paid ₹21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

---

Common Mistakes

❌ Incorrect formation of equations.

❌ Sign errors during elimination.

❌ Forgetting to substitute back to find the second variable.

❌ Making calculation mistakes while multiplying equations.

❌ Writing the final answer without units.

---

Exam Tips

✔ Define variables clearly.

✔ Write equations neatly.

✔ Eliminate the variable with smaller coefficients.

✔ Verify your answer by substitution.

✔ Always write the final answer in a sentence.

---

Practice MCQs

Q1.

The solution of x + y = 5 and x − y = 1 is:

A. (3, 2)

B. (2, 3)

C. (1, 4)

D. (4, 1)

Answer: A

---

Q2.

The pair of equations 2x + 3y = 6 and 4x + 6y = 12 has:

A. Unique solution

B. No solution

C. Infinite solutions

D. Two solutions

Answer: C

---

Q3.

If x + y = 10 and x − y = 4, then y equals:

A. 2

B. 3

C. 4

D. 5

Answer: B

---

Frequently Asked Questions (FAQ)

Q1. Which methods are used in Exercise 3.3?

Elimination Method and Substitution Method.

Q2. Which method is better?

It depends on the coefficients of the equations. Choose the method that makes calculations easier.

Q3. Are word problems important for board exams?

Yes. Word problems are frequently asked in board examinations.

Q4. How can I avoid mistakes?

Practice equation formation and verify your answers after solving.

---

Conclusion

Exercise 3.3 teaches students how to solve a pair of linear equations algebraically and apply these concepts to real-life situations such as age problems, digit problems, and money-related questions.

---

Call To Action (CTA)

📚 Looking for more NCERT Solutions, Important Questions, Notes, and Mock Tests?

🌐 Visit: www.mymockmate.com

🎯 Learn Better • Practice More • Score Higher with MyMockMate