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0580/23 Oct/Nov 2025, Question 27: Simultaneous Equations by Elimination

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 6 marks

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The question, in short

Solve the simultaneous equations y = x² − 8x + 22 and y + 2 = 3x, giving the values of x and y that satisfy both.

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Solution · 6 marks

  1. 1y = 3x − 2, so x² − 8x + 22 = 3x − 2
  2. 2x² − 11x + 24 = 0
  3. 3(x − 3)(x − 8) = 0, so x = 3 or x = 8
  4. 4y = 3 × 3 − 2 = 7 and y = 3 × 8 − 2 = 22
  5. 5x = 3, y = 7 and x = 8, y = 22

Answerx = 3, y = 7 and x = 8, y = 22

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Also searched as: 0580/23/O/N/25 · 0580_w25_qp_23 · 0580 w25 23 · question 27.
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