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Free · Class 9–10 · 5 worksheets · answer keys · practise online · set 2

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 2
Name:Date:Score:    / 8

Answer Yes or No.

  1. Is (0, 3) a solution of 5x + y = 3?
  2. Is (4, 1) a solution of 4x − 3y = 14?
  3. Is (−3, −4) a solution of 4x − 3y = 1?
  4. Is (1, −3) a solution of 2x − y = 5?
  5. Is (5, 5) a solution of 3x − 6y = −13?
  6. Is (1, −3) a solution of 6x + 3y = −2?
  7. Is (0, −2) a solution of x − 6y = 15?
  8. Is (−2, 1) a solution of 3x − 5y = −9?

Find k

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

Find the value of k.

  1. x = 5, y = −4 is a solution of 6x + ky = 34. Find k.
  2. x = 1, y = 1 is a solution of 6x + ky = 1. Find k.
  3. x = −3, y = −2 is a solution of 1x + ky = −7. Find k.
  4. x = 0, y = −5 is a solution of 3x + ky = −5. Find k.
  5. x = −3, y = 3 is a solution of 4x + ky = −24. Find k.
  6. x = −4, y = −2 is a solution of 1x + ky = 4. Find k.
  7. x = 5, y = −3 is a solution of 1x + ky = −7. Find k.
  8. x = −1, y = 5 is a solution of 6x + ky = −36. Find k.

Find y

Class 9 · Worksheet 3 · set 2
Name:Date:Score:    / 8

Find the value of y.

  1. For x − 6y = −24, find y when x = 0.
  2. For 5x − 4y = −3, find y when x = −3.
  3. For x + y = −6, find y when x = −1.
  4. For 2x − 4y = −2, find y when x = 3.
  5. For 5x + 6y = −21, find y when x = −3.
  6. For 4x − 4y = −4, find y when x = 3.
  7. For x − 2y = 4, find y when x = −4.
  8. For 6x + 6y = −54, find y when x = −6.

Solve the pair of equations

Class 10 · Worksheet 4 · set 2
Name:Date:Score:    / 8

Solve by substitution or elimination.

  1. 3x + 2y = −36; −x − y = 14
  2. −2x − 2y = −8; −x + y = −6
  3. 2x − 4y = 16; x − 5y = 26
  4. 3x + 4y = −44; 5x − 5y = −15
  5. −3x + 4y = 15; −x − 5y = −14
  6. 2x + 4y = 36; −2x + 3y = 6
  7. 4x + 4y = 32; −5x − 3y = −30
  8. 3x − 5y = −31; 5x + 2y = −31

Word problems

Class 10 · Worksheet 5 · set 2
Name:Date:Score:    / 6

Form two equations and solve.

  1. Riya has 20 coins of ₹5 and ₹10, worth ₹180 in all. How many of each coin does she have?
  2. 2 pens and 3 pencils cost ₹57. 1 pen and 2 pencils cost ₹32. Find the cost of one pen and one pencil.
  3. The sum of two numbers is 56 and their difference is 42. Find the numbers.
  4. 2 pens and 3 pencils cost ₹42. 1 pen and 2 pencils cost ₹22. Find the cost of one pen and one pencil.
  5. The sum of two numbers is 58 and their difference is 22. Find the numbers.
  6. 2 pens and 3 pencils cost ₹66. 1 pen and 2 pencils cost ₹38. 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.