4MA1/2HR Jun 2023, Question 21: Simultaneous Equations with a Curve
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks
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The question, in short
Find the coordinates where the line y − 2x = 1 meets the curve y² + xy = 7, showing clear algebraic working.
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Solution · 5 marks
- 1y = 2x + 1
- 2substitute into second equation: (2x + 1)² + x(2x + 1) = 7
- 3(4x² + 4x + 1) + (2x² + x) = 7
- 46x² + 5x + 1 = 7
- 56x² + 5x − 6 = 0
- 6(2x + 3)(3x − 2) = 0
- 7x = −3/2 or x = 2/3
- 8when x = −3/2, y = 2(−3/2) + 1 = −3 + 1 = −2
- 9when x = 2/3, y = 2(2/3) + 1 = 4/3 + 3/3 = 7/3
- 10(−3/2, −2) (2/3, 7/3)
Answer(−3/2, −2) (2/3, 7/3)
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