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Free · Class 9–10 · 5 worksheets · answer keys · practise online · set 97

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 97
Name:Date:Score:    / 8

Answer Yes or No.

  1. Is (−3, 1) a solution of x + 3y = 3?
  2. Is (1, 0) a solution of 2x + 4y = 2?
  3. Is (−5, 2) a solution of x + 4y = 6?
  4. Is (−2, 2) a solution of 3x + 4y = 3?
  5. Is (2, 4) a solution of 4x − 6y = −16?
  6. Is (−4, 1) a solution of x + 2y = −2?
  7. Is (5, −2) a solution of 3x + 5y = 8?
  8. Is (−1, −2) a solution of 6x + 6y = −18?

Find k

Class 9 · Worksheet 2 · set 97
Name:Date:Score:    / 8

Find the value of k.

  1. x = −4, y = −5 is a solution of 3x + ky = −42. Find k.
  2. x = −4, y = 4 is a solution of 2x + ky = 8. Find k.
  3. x = −4, y = 1 is a solution of 3x + ky = −17. Find k.
  4. x = −1, y = 2 is a solution of 1x + ky = −11. Find k.
  5. x = 0, y = −5 is a solution of 2x + ky = −10. Find k.
  6. x = 4, y = −4 is a solution of 1x + ky = 8. Find k.
  7. x = −2, y = −4 is a solution of 3x + ky = −14. Find k.
  8. x = 1, y = 1 is a solution of 5x + ky = 11. Find k.

Find y

Class 9 · Worksheet 3 · set 97
Name:Date:Score:    / 8

Find the value of y.

  1. For 2x + 4y = 4, find y when x = −4.
  2. For 6x − 4y = −8, find y when x = −2.
  3. For 6x − 2y = 8, find y when x = 1.
  4. For 3x − 2y = −14, find y when x = −4.
  5. For 3x − y = 5, find y when x = 1.
  6. For 4x − 2y = 12, find y when x = 2.
  7. For x − 4y = −20, find y when x = −4.
  8. For 6x + y = 34, find y when x = 5.

Solve the pair of equations

Class 10 · Worksheet 4 · set 97
Name:Date:Score:    / 8

Solve by substitution or elimination.

  1. 3x − 3y = 18; −3x − 2y = −28
  2. −4x − 4y = 48; 5x + 2y = −39
  3. −x + 5y = −15; x + 4y = −3
  4. −x + 3y = −1; −5x − 5y = −5
  5. 4x + 5y = −16; x + y = −3
  6. x − 3y = 26; 5x + 5y = 10
  7. −x + 3y = 29; 5x + y = −17
  8. −4x − 4y = 8; 2x − 4y = −10

Word problems

Class 10 · Worksheet 5 · set 97
Name:Date:Score:    / 6

Form two equations and solve.

  1. 2 pens and 3 pencils cost ₹67. 1 pen and 2 pencils cost ₹38. Find the cost of one pen and one pencil.
  2. 2 pens and 3 pencils cost ₹24. 1 pen and 2 pencils cost ₹13. Find the cost of one pen and one pencil.
  3. 2 pens and 3 pencils cost ₹41. 1 pen and 2 pencils cost ₹25. Find the cost of one pen and one pencil.
  4. 2 pens and 3 pencils cost ₹51. 1 pen and 2 pencils cost ₹30. Find the cost of one pen and one pencil.
  5. The sum of two numbers is 105 and their difference is 11. Find the numbers.
  6. 2 pens and 3 pencils cost ₹39. 1 pen and 2 pencils cost ₹21. 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.