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4024/13 May/Jun 2026, Question 13: Simultaneous Equations by Elimination

Cambridge O Level Mathematics 4024 · Paper 13 (Non-calculator) · Non-calculator · 7 marks

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The question, in short

Solve two problems: a pair of simultaneous equations showing all working, and a quadratic equation by factorisation.

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Part (a) · 4 marks

Solve 5x − 2y = 19 and 2x − 3y = 1 simultaneously, showing all working.

  1. 1×3: 15x − 6y = 57; ×2: 4x − 6y = 2
  2. 2Subtract: 11x = 55, so x = 5
  3. 35(5) − 2y = 19, so 2y = 6
  4. 4y = 3

Answerx = 5, y = 3

Part (b) · 3 marks

Solve 6x² − x − 5 = 0 by factorisation.

  1. 16x² − 6x + 5x − 5 = 0
  2. 26x(x − 1) + 5(x − 1) = 0
  3. 3(6x + 5)(x − 1) = 0
  4. 4x = −5/6 or x = 1

Answerx = −5/6 or x = 1

Stuck on a step? Read the free lesson: Simultaneous Equations by Elimination

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Also searched as: 4024/13/M/J/26 · 4024_s26_qp_13 · 4024 s26 13 · question 13.
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