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0580/43 May/Jun 2021, Question 5: Simultaneous Equations with a Curve

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 6 marks

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The question, in short

Solve two pairs of simultaneous equations: one linear pair in x and y, and one pair combining a line with a quadratic.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Solve the linear simultaneous equations x + 2y = 13 and x + 5y = 22 for x and y.

  1. 1Subtract: (x + 5y) − (x + 2y) = 22 − 13, so 3y = 9
  2. 2y = 3
  3. 3x = 13 − 2 × 3 = 7
  4. 4x = 7, y = 3

Answerx = 7, y = 3

Part (b) · 4 marks

Solve the simultaneous equations y = 2 − x and y = x² + 2x + 2 for x and y.

  1. 12 − x = x² + 2x + 2
  2. 2x² + 3x = 0
  3. 3x(x + 3) = 0, so x = 0 or x = −3
  4. 4x = 0: y = 2 − 0 = 2; x = −3: y = 2 + 3 = 5
  5. 5x = 0, y = 2 and x = −3, y = 5

Answerx = 0, y = 2 and x = −3, y = 5

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Also searched as: 0580/43/M/J/21 · 0580_s21_qp_43 · 0580 s21 43 · question 5.
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