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🧾 CBSE · Class 10

Class 10 Maths: Pair of Linear Equations in Two Variables Worksheet (with Answers)

A free, print-ready worksheet on Pair of Linear Equations in Two Variables for CBSE Class 10 Maths, with a matching answer key. Use the sample below, or build your own with the exact mix of questions you need — no login, no ads.

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Sample worksheet

7 of 17 questions from this chapter. Generate your own for the full set, more variations, and a clean print layout.

  1. 1. The pair x + 2y = 4 and 2x + 4y = 12 has:
    • (a) a unique solution
    • (b) exactly two solutions
    • (c) no solution
    • (d) infinitely many solutions
  2. 2. If a₁/a₂ ≠ b₁/b₂, the pair has:
    • (a) a unique solution
    • (b) no solution
    • (c) no real meaning
    • (d) infinitely many solutions
  3. 3. The solution of x + y = 5 and x − y = 1 is:
    • (a) (4, 1)
    • (b) (3, 2)
    • (c) (2, 3)
    • (d) (1, 4)
  4. 4. Two lines coincide when:
    • (a) a₁/a₂ = b₁/b₂ = c₁/c₂
    • (b) they are perpendicular
    • (c) a₁/a₂ ≠ b₁/b₂
    • (d) a₁/a₂ = b₁/b₂ ≠ c₁/c₂
  5. 5. Is the pair 2x + 3y = 7 and 4x + 6y = 14 consistent?
  6. 6. Solve 2x = y and x + y = 6.
  7. 7. Solve 3x − 5y = −2 and 2x + y = 4 by elimination.
View answers
  1. 1. (c) no solution — 1/2 = 2/4 ≠ −4/−12, so the lines are parallel — no solution.
  2. 2. (a) a unique solution — Unequal ratios of x and y coefficients ⇒ intersecting lines ⇒ unique solution.
  3. 3. (b) (3, 2) — Adding gives 2x = 6, x = 3, y = 2.
  4. 4. (a) a₁/a₂ = b₁/b₂ = c₁/c₂ — All three ratios equal ⇒ coincident lines ⇒ infinitely many solutions.
  5. 5. Ratios: 2/4 = 3/6 = 7/14 = 1/2, so the lines coincide — consistent with infinitely many solutions.
  6. 6. Substitute y = 2x: x + 2x = 6 ⇒ x = 2, y = 4.
  7. 7. Multiply the second by 5: 10x + 5y = 20. Add to the first: 13x = 18 ⇒ x = 18/13. Hmm; instead multiply second by 5 and add: 3x − 5y = −2 and 10x + 5y = 20 give 13x = 18, x = 18/13, then y = 4 − 2(18/13) = (52 − 36)/13 = 16/13. Solution: (18/13, 16/13).
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FAQ

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Does the Pair of Linear Equations in Two Variables worksheet come with answers?
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Can I choose how many questions and which types?
Yes. Open the generator for this chapter and set how many MCQs, short, long and HOTS questions you want; totals and marks update live, and you can swap any single question.
Which board and class is this for?
This worksheet is aligned to CBSE Class 10 Maths, chapter “Pair of Linear Equations in Two Variables”.