4MA1/2HR Jan 2023, Question 22: 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
Solve the simultaneous equations 2y² + x² = −6x + 42 and 2x + y = −3, showing clear algebraic working.
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Solution · 5 marks
- 1From 2x + y = −3: y = −3 − 2x
- 2Substitute: 2(−3 − 2x)² + x² = −6x + 42, so 9x² + 24x + 18 = −6x + 42
- 39x² + 30x − 24 = 0, so 3x² + 10x − 8 = 0
- 4(3x − 2)(x + 4) = 0, so x = 2/3 or x = −4
- 5y = −3 − 2x gives x = −4, y = 5 and x = 2/3, y = −13/3
Answerx = −4, y = 5 and x = 2/3, y = −13/3
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