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Solving a pair of equations by elimination: Class 10 practice

Make the coefficients of one variable equal (multiply one or both equations), then add or subtract to eliminate it. Read the method, follow the three worked examples, then try the six questions.

What you should know first

  • Solving linear equations

The idea behind solving a pair of equations by elimination

Make the coefficients of one variable equal (multiply one or both equations), then add or subtract to eliminate it. Solve for the other variable and substitute back.

Step-by-step method

  1. Multiply so one variable has matching coefficients.
  2. Add or subtract to eliminate it.
  3. Solve for the remaining variable.
  4. Substitute back and check both equations.

Worked example 1 (Basic)

Solve: 4x + 2y = 2 and 3x + 4y = 14.

  1. Eliminate one variable by matching coefficients
  2. x = -2
  3. y = 5
  4. Check: 4(-2) + 10 = 2 ✓
  5. Answer: x = -2, y = 5

Worked example 2 (Standard)

Solve: 5x − 5y = -20 and 3x + 6y = 33.

  1. Eliminate one variable by matching coefficients
  2. x = 1
  3. y = 5
  4. Check: 5(1) − 25 = -20 ✓
  5. Answer: x = 1, y = 5

Worked example 3 (Challenge)

Solve: 3x − 5y = -1 and 6x + 2y = -14.

  1. Eliminate one variable by matching coefficients
  2. x = -2
  3. y = -1
  4. Check: 3(-2) + 5 = -1 ✓
  5. Answer: x = -2, y = -1

Common mistakes and misconceptions

  • Subtracting only some terms
  • Forgetting to multiply the constant

Practice questions

  1. (Basic) Solve: 3x + 3y = 15 and 1x + 4y = 26.
  2. (Basic) Solve: 3x + 1y = 0 and 5x + 4y = 14.
  3. (Standard) Solve: 1x − 3y = 5 and 5x + 1y = 9.
  4. (Standard) Solve: 3x − 1y = -12 and 1x + 3y = -4.
  5. (Challenge) Solve: 5x − 2y = 9 and 3x + 2y = 15.
  6. (Challenge) Solve: 3x − 1y = 7 and 5x + 2y = -3.

Answer key with full working

  • Q1: Eliminate one variable by matching coefficients → x = -2 → y = 7 → Check: 3(-2) + 21 = 15 ✓ → Answer: x = -2, y = 7
  • Q2: Eliminate one variable by matching coefficients → x = -2 → y = 6 → Check: 3(-2) + 6 = 0 ✓ → Answer: x = -2, y = 6
  • Q3: Eliminate one variable by matching coefficients → x = 2 → y = -1 → Check: 1(2) + 3 = 5 ✓ → Answer: x = 2, y = -1
  • Q4: Eliminate one variable by matching coefficients → x = -4 → y = 0 → Check: 3(-4) + 0 = -12 ✓ → Answer: x = -4, y = 0
  • Q5: Eliminate one variable by matching coefficients → x = 3 → y = 3 → Check: 5(3) − 6 = 9 ✓ → Answer: x = 3, y = 3
  • Q6: Eliminate one variable by matching coefficients → x = 1 → y = -4 → Check: 3(1) + 4 = 7 ✓ → Answer: x = 1, y = -4

Syllabus note

This skill is listed under "Pair of Linear Equations" for Class 10 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

Related practice and notes

Frequently asked questions

Which chapter is solving a pair of equations by elimination in?

"Pair of Linear Equations", Class 10 Maths (NCERT/CBSE). Other boards may place it differently.

How were the answers checked?

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

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