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Free · Class 9–10 · 5 worksheets · answer keys · practise online · set 21

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 21
Name:Date:Score:    / 8

Answer Yes or No.

  1. Is (−4, −1) a solution of x + 5y = −6?
  2. Is (4, 3) a solution of x − 3y = −4?
  3. Is (1, 2) a solution of 6x − y = 4?
  4. Is (−1, −1) a solution of 2x + 6y = −6?
  5. Is (2, 5) a solution of 5x + 5y = 35?
  6. Is (−1, −2) a solution of 6x − y = −3?
  7. Is (0, −2) a solution of 6x − 3y = 7?
  8. Is (0, 4) a solution of 2x + y = 7?

Find k

Class 9 · Worksheet 2 · set 21
Name:Date:Score:    / 8

Find the value of k.

  1. x = 3, y = −3 is a solution of 6x + ky = 33. Find k.
  2. x = −2, y = 2 is a solution of 5x + ky = 2. Find k.
  3. x = −2, y = 3 is a solution of 1x + ky = 16. Find k.
  4. x = 2, y = 1 is a solution of 4x + ky = 13. Find k.
  5. x = −4, y = 2 is a solution of 6x + ky = −16. Find k.
  6. x = −2, y = 3 is a solution of 1x + ky = −8. Find k.
  7. x = −3, y = 4 is a solution of 6x + ky = −38. Find k.
  8. x = 0, y = 4 is a solution of 2x + ky = 24. Find k.

Find y

Class 9 · Worksheet 3 · set 21
Name:Date:Score:    / 8

Find the value of y.

  1. For 2x − 6y = 12, find y when x = −3.
  2. For 6x − y = −25, find y when x = −5.
  3. For 2x + y = 4, find y when x = 1.
  4. For x − 3y = 1, find y when x = −2.
  5. For 2x + 3y = −8, find y when x = −4.
  6. For 2x + y = −10, find y when x = −3.
  7. For 4x − 5y = −33, find y when x = −2.
  8. For 2x + 6y = 12, find y when x = 6.

Solve the pair of equations

Class 10 · Worksheet 4 · set 21
Name:Date:Score:    / 8

Solve by substitution or elimination.

  1. −x + 2y = −11; −3x + 4y = −29
  2. x + y = 15; x − y = −1
  3. −3x + 5y = −44; −4x + 5y = −47
  4. −4x + 4y = 28; −5x − 5y = 15
  5. −4x − 4y = 44; 3x − 5y = −1
  6. −4x + 3y = −15; −4x + 4y = −20
  7. 4x + 5y = −50; 2x − 2y = 2
  8. −5x + y = −18; −x − 5y = 12

Word problems

Class 10 · Worksheet 5 · set 21
Name:Date:Score:    / 6

Form two equations and solve.

  1. 2 pens and 3 pencils cost ₹53. 1 pen and 2 pencils cost ₹30. Find the cost of one pen and one pencil.
  2. 2 pens and 3 pencils cost ₹52. 1 pen and 2 pencils cost ₹29. Find the cost of one pen and one pencil.
  3. Riya has 27 coins of ₹5 and ₹10, worth ₹215 in all. How many of each coin does she have?
  4. The sum of two numbers is 56 and their difference is 2. Find the numbers.
  5. The sum of two numbers is 80 and their difference is 36. Find the numbers.
  6. 2 pens and 3 pencils cost ₹51. 1 pen and 2 pencils cost ₹28. Find the cost of one pen and one pencil.

More worksheets

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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.