Pair Linear Equations Exemplar — Class 10 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Pair Linear Equations Exemplar" — 5 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Pair Linear Equations Exemplar" — 5 important questions with detailed answers for…
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NCERT Solutions for Class 10 Mathematics — Pair Linear Equations Exemplar. Step-by-step answers to all 5 textbook questions from this chapter, written for CBSE board preparation and free to use.
Pair Linear Equations Exemplar — All 5 Questions Solved
Q1. Solve graphically: x + y = 4 and 2x - y = 2.
From x + y = 4: y = 4 - x. Points: (0,4), (4,0). From 2x - y = 2: y = 2x - 2. Points: (0,-2), (1,0). Lines intersect at (2,2). Solution: x = 2, y = 2.
Q2. Solve using elimination: 3x + 2y = 8 and 5x - 2y = 4.
Add equations: 8x = 12, so x = 3/2. Substitute: 3(3/2) + 2y = 8. So 9/2 + 2y = 8, giving 2y = 7/2, thus y = 7/4.
Q3. Solve using substitution: x + 2y = 7 and 2x - y = 4.
From first: x = 7 - 2y. Substitute in second: 2(7 - 2y) - y = 4. So 14 - 4y - y = 4, giving 5y = 10, thus y = 2. Then x = 7 - 4 = 3.
Q4. For what value of k does the system 2x + 3y = 5 and kx + 6y = 10 have infinite solutions?
For infinite solutions: a1/a2 = b1/b2 = c1/c2. So 2/k = 3/6 = 5/10. From 3/6 = 1/2, we need 2/k = 1/2, thus k = 4.
Q5. Two angles are supplementary. If one is 20° more than the other, find both angles.
Let angles be x and x + 20. Since supplementary: x + (x + 20) = 180. So 2x + 20 = 180, giving x = 80. Angles are 80° and 100°.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.