{"id":4987,"date":"2026-06-21T11:44:11","date_gmt":"2026-06-21T06:14:11","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=4987"},"modified":"2026-06-21T12:45:24","modified_gmt":"2026-06-21T07:15:24","slug":"ncert-class-10-maths-exercise-3-2-solutions-pair-of-linear-equations","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-10-maths-exercise-3-2-solutions-pair-of-linear-equations\/","title":{"rendered":"NCERT Class 10 Maths Exercise 3.2 Solutions | Pair of Linear Equations"},"content":{"rendered":"
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Short Introduction<\/h1>\n\n\n\n

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

These solutions are prepared in a simple, step-by-step manner to help students understand the concepts clearly and score better in examinations.<\/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>3.2<\/td><\/tr>
Method Used<\/td>Substitution Method<\/td><\/tr>
Board<\/td>CBSE & State Boards<\/td><\/tr>
Difficulty Level<\/td>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

✔ Substitution Method<\/p>\n\n\n\n

✔ Solving Real-Life Word Problems<\/p>\n\n\n\n

✔ Verification of Solutions<\/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>

✔ Forming Equations from Statements<\/p>\n\n\n\n

✔ Application of Linear Equations<\/p>\n\n\n\n

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

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

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

Steps of Substitution Method<\/h3>\n\n\n\n
    \n
  1. Express one variable in terms of another.<\/li>\n\n\n\n
  2. Substitute it into the second equation.<\/li>\n\n\n\n
  3. Solve the resulting equation.<\/li>\n\n\n\n
  4. Substitute back to find the second variable.<\/li>\n\n\n\n
  5. Verify the answer.<\/li>\n<\/ol>\n\n\n\n
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    Question 1 Solve the following pair of linear equations by the substitution method.<\/h1>\n\n\n\n

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

    x + y = 14<\/p>\n\n\n\n

    x − y = 4<\/p>\n\n\n\n

    Solution<\/h3>\n\n\n\n
    \"\"<\/figure>\n\n\n\n
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    Question 1 (ii)<\/h1>\n\n\n\n
    Related Topic to Read more<\/span>NCERT Class 10 Maths Exercise 2.1 Solutions | Polynomials<\/span><\/a><\/div>

    Solve:<\/p>\n\n\n\n

    s − t = 3<\/p>\n\n\n\n

    s\/3 + t\/2 = 6<\/p>

    \"\"<\/a><\/div><\/div>\n\n\n\n

    Solution<\/h3>\n\n\n\n
    \"\"<\/figure>\n\n\n\n
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    Question 1 (iii)<\/h1>\n\n\n\n

    Solve:<\/p>\n\n\n\n

    3x − y = 3<\/p>\n\n\n\n

    9x − 3y = 9<\/p>\n\n\n\n

    Solution<\/h3>\n\n\n\n
    \"\"<\/figure>\n\n\n\n
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    Question 1 (iv)<\/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>

    Solve:<\/p>\n\n\n\n

    0.2x + 0.3y = 1.3<\/p>\n\n\n\n

    0.4x + 0.5y = 2.3<\/p>\n\n\n\n

    Solution<\/h3>\n\n\n\n
    \"\"<\/figure>\n\n\n\n
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    Question 1 (v)<\/h1>\n\n\n\n

    Solve:<\/p>\n\n\n\n

    √2x + √3y = 0<\/p>\n\n\n\n

    √3x − √8y = 0<\/p>\n\n\n\n

    <\/h3>\n\n\n\n
    \"\"<\/figure>\n\n\n\n
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    Question 1 (vi)<\/h1>\n\n\n\n

    Solve:<\/p>\n\n\n\n

    3x\/2 − 5y\/3 = −2<\/p>\n\n\n\n

    x\/3 + y\/2 = 13\/6<\/p>\n\n\n\n

    <\/h3>\n\n\n\n
    \"\"<\/figure>\n\n\n\n
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    Question 2 Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.<\/h1>\n\n\n\n

    Solve:<\/p>\n\n\n\n

    2x + 3y = 11<\/p>\n\n\n\n

    2x − 4y = −24<\/p>\n\n\n\n

    Solution<\/h3>\n\n\n\n
    \"\"<\/figure>\n\n\n\n
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    Question 3 Form the pair of linear equations for the following problems and find their solution by
    substitution method.<\/h1>\n\n\n\n

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

    Solution<\/h3>\n\n\n\n
    \"\"<\/figure>\n\n\n\n
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    Question 3 (ii)<\/h1>\n\n\n\n

    The larger of two supplementary angles exceeds the smaller by 18 degrees. Find
    them.<\/strong><\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n
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    Question 3 (iii)<\/h1>\n\n\n\n

    The coach of a cricket team buys 7 bats and 6 balls for ₹3800. Later, she buys 3 bats and 5 balls for<\/code> ₹1750. Find the cost of each bat and each ball.<\/strong><\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n
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    Question 3 (iv)<\/h1>\n\n\n\n

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

    \"\"<\/figure>\n\n\n\n

    Question 3 (v)<\/h1>\n\n\n\n

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

    \"\"<\/figure>\n\n\n\n
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    Question 3 (vi)<\/h1>\n\n\n\n

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

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

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

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

    ❌ Forgetting to verify the answer.<\/p>\n\n\n\n

    ❌ Errors in simplifying fractions.<\/p>\n\n\n\n

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

    ✅ Write equations clearly.<\/p>\n\n\n\n

    ✅ Use substitution carefully.<\/p>\n\n\n\n

    ✅ Verify the final answer.<\/p>\n\n\n\n

    ✅ Mention units wherever required.<\/p>\n\n\n\n

    ✅ Practice word problems regularly.<\/p>\n\n\n\n

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

    1. The solution of x + y = 8 and x − y = 2 is:<\/h3>\n\n\n\n

    A. (5,3)<\/p>\n\n\n\n

    B. (3,5)<\/p>\n\n\n\n

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

    D. (6,2)<\/p>\n\n\n\n

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

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    2. Coincident lines have:<\/h3>\n\n\n\n

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

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

    C. Infinitely many 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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    3. In substitution method, the first step is:<\/h3>\n\n\n\n

    A. Draw the graph<\/p>\n\n\n\n

    B. Eliminate variables<\/p>\n\n\n\n

    C. Express one variable in terms of another<\/p>\n\n\n\n

    D. Add equations<\/p>\n\n\n\n

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

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

    Q1. Which method is used in Exercise 3.2?<\/h3>\n\n\n\n

    The Substitution Method.<\/p>\n\n\n\n

    Q2. Are these questions important for board exams?<\/h3>\n\n\n\n

    Yes, they are frequently asked.<\/p>\n\n\n\n

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

    Yes, they carry good marks in examinations.<\/p>\n\n\n\n

    Q4. How many marks can be expected from this chapter?<\/h3>\n\n\n\n

    Generally, 4–6 marks.<\/p>\n\n\n\n

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

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

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    📚 Looking for more NCERT Solutions, Mock Tests, Notes, Previous Year Questions, and Exam Preparation Resources?<\/p>\n\n\n\n

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

    🚀 Learn Better. Practice More. Score Higher.<\/p>\n\n\n\n

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