4MA1/2H Jun 2020, Question 16: Simultaneous Equations with a Curve
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks
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The question, in short
Solve the simultaneous equations 3xy − y² = 8 and x − 2y = 1, showing clear algebraic working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1From x − 2y = 1: x = 1 + 2y
- 2Substitute: 3(1 + 2y)y − y² = 8, so 5y² + 3y − 8 = 0
- 3(5y + 8)(y − 1) = 0, so y = −8/5 or y = 1
- 4x = 1 + 2y gives x = −11/5 or x = 3
- 5x = −11/5, y = −8/5; x = 3, y = 1
Answerx = −11/5, y = −8/5; x = 3, y = 1
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