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Free · Class 9–10 · 5 worksheets · answer keys · practise online · set 24

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 24
Name:Date:Score:    / 8

Answer Yes or No.

  1. Is (−3, 1) a solution of 4x + 3y = −9?
  2. Is (−3, 1) a solution of 4x − 3y = −12?
  3. Is (−5, 3) a solution of 4x − 6y = −36?
  4. Is (3, 5) a solution of 5x − y = 10?
  5. Is (4, 0) a solution of 5x + 2y = 22?
  6. Is (1, 4) a solution of 3x − y = −1?
  7. Is (−4, 4) a solution of 6x + 3y = −12?
  8. Is (1, 1) a solution of 5x + 2y = 10?

Find k

Class 9 · Worksheet 2 · set 24
Name:Date:Score:    / 8

Find the value of k.

  1. x = −2, y = −2 is a solution of 1x + ky = 4. Find k.
  2. x = −4, y = −4 is a solution of 2x + ky = 12. Find k.
  3. x = 1, y = −2 is a solution of 1x + ky = 7. Find k.
  4. x = 5, y = −3 is a solution of 4x + ky = 17. Find k.
  5. x = 5, y = −2 is a solution of 4x + ky = 30. Find k.
  6. x = −2, y = −4 is a solution of 5x + ky = −22. Find k.
  7. x = −5, y = 4 is a solution of 4x + ky = −4. Find k.
  8. x = −5, y = 4 is a solution of 4x + ky = −36. Find k.

Find y

Class 9 · Worksheet 3 · set 24
Name:Date:Score:    / 8

Find the value of y.

  1. For x + y = 4, find y when x = 4.
  2. For 5x + 4y = −11, find y when x = 1.
  3. For x − 5y = −13, find y when x = 2.
  4. For 4x − y = 20, find y when x = 5.
  5. For 2x − y = −9, find y when x = −5.
  6. For 6x − 2y = −6, find y when x = 1.
  7. For 4x + 4y = −8, find y when x = −5.
  8. For 4x + 2y = −14, find y when x = −5.

Solve the pair of equations

Class 10 · Worksheet 4 · set 24
Name:Date:Score:    / 8

Solve by substitution or elimination.

  1. −5x + 4y = −3; 3x − 3y = 0
  2. 5x + 2y = 22; 2x + 5y = 34
  3. −5x + 4y = −23; −3x + 2y = −11
  4. −4x + y = 16; 2x − y = −6
  5. 3x − y = 5; 3x − 3y = −9
  6. −3x − 2y = −22; −x − 2y = −6
  7. 2x + 2y = 6; x + 5y = −1
  8. −3x − 5y = −30; −x − 2y = −11

Word problems

Class 10 · Worksheet 5 · set 24
Name:Date:Score:    / 6

Form two equations and solve.

  1. 2 pens and 3 pencils cost ₹61. 1 pen and 2 pencils cost ₹35. Find the cost of one pen and one pencil.
  2. Riya has 19 coins of ₹5 and ₹10, worth ₹155 in all. How many of each coin does she have?
  3. Riya has 33 coins of ₹5 and ₹10, worth ₹255 in all. How many of each coin does she have?
  4. 2 pens and 3 pencils cost ₹20. 1 pen and 2 pencils cost ₹11. Find the cost of one pen and one pencil.
  5. Riya has 31 coins of ₹5 and ₹10, worth ₹225 in all. How many of each coin does she have?
  6. 2 pens and 3 pencils cost ₹26. 1 pen and 2 pencils cost ₹14. 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.