4MA1/2H Jun 2024, Question 22: 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 line x + y = 5 together with the curve 2x² + 3y² = 210 to find the coordinates of their intersection points, showing algebraic working.
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Solution · 5 marks
- 1Substitute y = 5 − x: 2x² + 3(5 − x)² = 210.
- 2Expand: 5x² − 30x + 75 = 210, so x² − 6x − 27 = 0.
- 3(x − 9)(x + 3) = 0, so x = 9 or x = −3.
- 4y = 5 − x gives y = −4 or y = 8: (9, −4) (−3, 8)
Answer(9, −4) (−3, 8)
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