4MA1/2H Jun 2019, Question 20: 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 y = 9 − x with the curve x² − 3xy + 2y² = 0 to find the coordinates of their two intersection points, showing algebraic working.
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Solution · 5 marks
- 1Substitute y = 9 − x: x² − 3x(9 − x) + 2(9 − x)² = 0
- 2x² − 27x + 3x² + 162 − 36x + 2x² = 0
- 36x² − 63x + 162 = 0, so 2x² − 21x + 54 = 0
- 4(2x − 9)(x − 6) = 0, so x = 4.5 or x = 6
- 5y = 9 − x gives (4.5, 4.5) and (6, 3)
Answer(4.5, 4.5) and (6, 3)
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