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Free · Class 9–10 · 5 worksheets · answer keys · practise online · set 52

Linear equations in two variables — Class 9 and 10 worksheets

Free linear equations in two variables worksheets: check a solution, find k, find y for a given x (Class 9), and solve a pair of linear equations with word problems (Class 10) — with answers.

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Is it a solution? (Class 9)Find k (Class 9)Find y (Class 9)Solve the pair of equations (Class 10)Word problems (Class 10)

Is it a solution?

Class 9 · Worksheet 1 · set 52
Name:Date:Score:    / 8

Answer Yes or No.

  1. Is (4, 0) a solution of 5x + 2y = 21?
  2. Is (−5, −1) a solution of 2x + 5y = −15?
  3. Is (4, −1) a solution of x − 5y = 10?
  4. Is (0, 3) a solution of 2x + 2y = 6?
  5. Is (−3, 1) a solution of 2x + y = −5?
  6. Is (2, 3) a solution of x − 5y = −11?
  7. Is (−2, 4) a solution of 4x − 6y = −31?
  8. Is (3, 1) a solution of 2x + 2y = 8?

Find k

Class 9 · Worksheet 2 · set 52
Name:Date:Score:    / 8

Find the value of k.

  1. x = −1, y = −3 is a solution of 4x + ky = 11. Find k.
  2. x = 1, y = 4 is a solution of 6x + ky = 10. Find k.
  3. x = 4, y = −2 is a solution of 5x + ky = 22. Find k.
  4. x = −3, y = 4 is a solution of 3x + ky = −5. Find k.
  5. x = 2, y = 2 is a solution of 6x + ky = 0. Find k.
  6. x = −4, y = −4 is a solution of 1x + ky = 8. Find k.
  7. x = −5, y = −2 is a solution of 4x + ky = −22. Find k.
  8. x = −1, y = 3 is a solution of 2x + ky = 16. Find k.

Find y

Class 9 · Worksheet 3 · set 52
Name:Date:Score:    / 8

Find the value of y.

  1. For 3x − 4y = 23, find y when x = 5.
  2. For 3x + 6y = 12, find y when x = −6.
  3. For 3x + 2y = 1, find y when x = −1.
  4. For 2x + 3y = −21, find y when x = −3.
  5. For 5x − 2y = 10, find y when x = 0.
  6. For 4x + 5y = 6, find y when x = −1.
  7. For 4x − 5y = 7, find y when x = 3.
  8. For x + 4y = −7, find y when x = 5.

Solve the pair of equations

Class 10 · Worksheet 4 · set 52
Name:Date:Score:    / 8

Solve by substitution or elimination.

  1. −x + 4y = −4; −2x + 2y = 10
  2. −5x + 2y = 9; −2x − 5y = −8
  3. 2x − y = −6; 3x − 2y = −8
  4. −x + 2y = −14; 2x + 4y = −20
  5. −5x + y = 10; 2x − 2y = −12
  6. −2x − y = 10; −3x + 3y = 33
  7. 3x − 3y = −18; −4x + 5y = 23
  8. −2x − 4y = −22; −5x + 2y = −7

Word problems

Class 10 · Worksheet 5 · set 52
Name:Date:Score:    / 6

Form two equations and solve.

  1. 2 pens and 3 pencils cost ₹35. 1 pen and 2 pencils cost ₹21. Find the cost of one pen and one pencil.
  2. Riya has 26 coins of ₹5 and ₹10, worth ₹230 in all. How many of each coin does she have?
  3. 2 pens and 3 pencils cost ₹47. 1 pen and 2 pencils cost ₹26. Find the cost of one pen and one pencil.
  4. 2 pens and 3 pencils cost ₹55. 1 pen and 2 pencils cost ₹32. Find the cost of one pen and one pencil.
  5. 2 pens and 3 pencils cost ₹40. 1 pen and 2 pencils cost ₹24. Find the cost of one pen and one pencil.
  6. 2 pens and 3 pencils cost ₹28. 1 pen and 2 pencils cost ₹16. Find the cost of one pen and one pencil.

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Questions

How many solutions does a linear equation in two variables have?

Infinitely many — every point on its straight-line graph is a solution. A pair of such equations usually has exactly one common solution.

Are these worksheets free?

Yes — print them or save as PDF free. Every worksheet has an answer key.

How do I get different questions?

Press “🔄 New set” — the questions change (maths numbers are new every time; English sentences are shuffled).

How do I print only one worksheet?

Press “🖨️ Print” on that worksheet. Tick “with answer key” if you want the answers on a second page.

Can my child do this worksheet online, like a quiz?

Yes — press “▶️ Practise online” on any worksheet. The questions come one at a time with instant marking, a score at the end and a review of mistakes. No sign-in is needed.