{"id":5030,"date":"2026-06-21T13:07:08","date_gmt":"2026-06-21T07:37:08","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=5030"},"modified":"2026-06-21T13:29:15","modified_gmt":"2026-06-21T07:59:15","slug":"ncert-class-10-maths-chapter-3-exercise-3-3-solutions-pair-of-linear-equations","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-10-maths-chapter-3-exercise-3-3-solutions-pair-of-linear-equations\/","title":{"rendered":"NCERT Class 10 Maths Chapter 3 Exercise 3.3 Solutions | Pair of Linear Equations"},"content":{"rendered":"
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Short Introduction<\/h1>\n\n\n\n

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<\/strong> and Substitution Method<\/strong>. This exercise also includes real-life word problems involving ages, fractions, numbers, money, and library charges.<\/p>\n\n\n\n

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Quick Information Box<\/h1>\n\n\n\n
Particular<\/th>Details<\/th><\/tr><\/thead>
Class<\/td>10<\/td><\/tr>
Subject<\/td>Mathematics<\/td><\/tr>
Chapter<\/td>Pair of Linear Equations in Two Variables<\/td><\/tr>
Exercise<\/td>3.3<\/td><\/tr>
Methods Used<\/td>Elimination Method and Substitution Method<\/td><\/tr>
Difficulty Level<\/td>Easy to Moderate<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
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Concepts Used (Topics Covered)<\/h1>\n\n\n\n

✔ Pair of Linear Equations in Two Variables<\/p>\n\n\n\n

✔ Elimination Method<\/p>\n\n\n\n

✔ Substitution Method<\/p>\n\n\n\n

✔ Formation of Equations<\/p>\n\n\n\n

✔ Age Problems<\/p>\n\n\n\n

Related Topic to Read more<\/span>NCERT Class 10 Maths Real Number Exercise 1.2 Solutions | MyMockMate<\/span><\/a><\/div>

✔ Digit Problems<\/p>\n\n\n\n

✔ Money Problems<\/p>\n\n\n\n

✔ Word Problems<\/p>\n\n\n\n

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Important Formulas<\/h1>\n\n\n\n

General Form of Linear Equation<\/h3>\n\n\n\n

ax + by + c = 0<\/p>\n\n\n\n

Unique Solution<\/h3>\n\n\n\n

a₁\/a₂ ≠ b₁\/b₂<\/p>\n\n\n\n

No Solution<\/h3>\n\n\n\n

a₁\/a₂ = b₁\/b₂ ≠ c₁\/c₂<\/p>\n\n\n\n

Infinitely Many Solutions<\/h3>\n\n\n\n
Related Topic to Read more<\/span>NCERT Class 10 Maths Exercise 2.1 Solutions | Polynomials<\/span><\/a><\/div>

a₁\/a₂ = b₁\/b₂ = c₁\/c₂<\/p>\n\n\n\n

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Question 1 Solve the following pair of linear equations by the elimination method and the substitution
method :<\/h1>\n\n\n\n

(i)<\/p>\n\n\n\n

x + y = 5<\/p>

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2x – 3y = 4<\/p>\n\n\n\n

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Question 1 (ii)<\/h1>\n\n\n\n

3x + 4y = 10<\/p>\n\n\n\n

2x − 2y = 2<\/p>\n\n\n\n

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Question 1 (iii)<\/h1>\n\n\n\n
Related Topic to Read more<\/span>Class 10 Maths Exercise 2.2 Solutions | Relationship Between Zeroes and Coefficients<\/span><\/a><\/div>

3x − 5y = 4<\/p>\n\n\n\n

9x − 2y = 7<\/p>\n\n\n\n

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Question 1 (iv)<\/h1>\n\n\n\n

x\/2 + 2y\/3 = −1<\/p>\n\n\n\n

x − y\/3 = 3<\/p>\n\n\n\n

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Question 2 (i)<\/h1>\n\n\n\n

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? <\/strong><\/p>\n\n\n\n

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Question 2 (ii)<\/h1>\n\n\n\n

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?<\/strong><\/p>\n\n\n\n

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Question 2 (iii)<\/h1>\n\n\n\n

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.<\/strong><\/p>\n\n\n\n

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Question 2 (iv)<\/h1>\n\n\n\n

Meena went to a bank to withdraw ₹2000. She asked the cashier to give her<\/code> ₹50 and ₹100 notes only. Meena got 25 notes in all. Find how many notes of<\/code> ₹50 and ₹100 she received.<\/strong><\/p>\n\n\n\n

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Question 2 (v)<\/h1>\n\n\n\n

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<\/code> ₹21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.<\/strong><\/p>\n\n\n\n

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Common Mistakes<\/h1>\n\n\n\n

❌ Incorrect formation of equations.<\/p>\n\n\n\n

❌ Sign errors during elimination.<\/p>\n\n\n\n

❌ Forgetting to substitute back to find the second variable.<\/p>\n\n\n\n

❌ Making calculation mistakes while multiplying equations.<\/p>\n\n\n\n

❌ Writing the final answer without units.<\/p>\n\n\n\n

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Exam Tips<\/h1>\n\n\n\n

✔ Define variables clearly.<\/p>\n\n\n\n

✔ Write equations neatly.<\/p>\n\n\n\n

✔ Eliminate the variable with smaller coefficients.<\/p>\n\n\n\n

✔ Verify your answer by substitution.<\/p>\n\n\n\n

✔ Always write the final answer in a sentence.<\/p>\n\n\n\n

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Practice MCQs<\/h1>\n\n\n\n

Q1.<\/h3>\n\n\n\n

The solution of x + y = 5 and x − y = 1 is:<\/p>\n\n\n\n

A. (3, 2)<\/p>\n\n\n\n

B. (2, 3)<\/p>\n\n\n\n

C. (1, 4)<\/p>\n\n\n\n

D. (4, 1)<\/p>\n\n\n\n

Answer:<\/strong> A<\/p>\n\n\n\n

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Q2.<\/h3>\n\n\n\n

The pair of equations 2x + 3y = 6 and 4x + 6y = 12 has:<\/p>\n\n\n\n

A. Unique solution<\/p>\n\n\n\n

B. No solution<\/p>\n\n\n\n

C. Infinite solutions<\/p>\n\n\n\n

D. Two solutions<\/p>\n\n\n\n

Answer:<\/strong> C<\/p>\n\n\n\n

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Q3.<\/h3>\n\n\n\n

If x + y = 10 and x − y = 4, then y equals:<\/p>\n\n\n\n

A. 2<\/p>\n\n\n\n

B. 3<\/p>\n\n\n\n

C. 4<\/p>\n\n\n\n

D. 5<\/p>\n\n\n\n

Answer:<\/strong> B<\/p>\n\n\n\n

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Frequently Asked Questions (FAQ)<\/h1>\n\n\n\n

Q1. Which methods are used in Exercise 3.3?<\/h3>\n\n\n\n

Elimination Method and Substitution Method.<\/p>\n\n\n\n

Q2. Which method is better?<\/h3>\n\n\n\n

It depends on the coefficients of the equations. Choose the method that makes calculations easier.<\/p>\n\n\n\n

Q3. Are word problems important for board exams?<\/h3>\n\n\n\n

Yes. Word problems are frequently asked in board examinations.<\/p>\n\n\n\n

Q4. How can I avoid mistakes?<\/h3>\n\n\n\n

Practice equation formation and verify your answers after solving.<\/p>\n\n\n\n

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Conclusion<\/h1>\n\n\n\n

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.<\/p>\n\n\n\n

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Call To Action (CTA)<\/h1>\n\n\n\n

📚 Looking for more NCERT Solutions, Important Questions, Notes, and Mock Tests?<\/p>\n\n\n\n

🌐 Visit: www.mymockmate.com<\/a><\/strong><\/p>\n\n\n\n

🎯 Learn Better • Practice More • Score Higher with MyMockMate<\/p>\n

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