4MA1/1HR Jun 2025, Question 22: Simultaneous Equations with a Curve
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
Solve the simultaneous equations x² + y² = 41 and 2x + y = 3, showing clear algebraic working.
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Solution · 5 marks
- 1y = 3 − 2x
- 2x² + (3 − 2x)² = 41
- 35x² − 12x + 9 = 41, so 5x² − 12x − 32 = 0
- 4(5x + 8)(x − 4) = 0
- 5x = 4 or x = −8/5
- 6x = 4: y = 3 − 8 = −5; x = −8/5: y = 3 + 16/5 = 31/5
Answerx = 4, y = −5 and x = −8/5, y = 31/5
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