4MA1/2HR Jun 2024, 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 x² + y² = y + 11 and y = 3x − 1, showing clear algebraic working.
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Solution · 5 marks
- 1Substitute y = 3x − 1: x² + (3x − 1)² = (3x − 1) + 11
- 2x² + 9x² − 6x + 1 = 3x + 10, so 10x² − 9x − 9 = 0
- 3(5x + 3)(2x − 3) = 0, so x = −0.6 or x = 1.5
- 4y = 3x − 1 gives y = −2.8 and y = 3.5
- 5x = −0.6, y = −2.8 and x = 1.5, y = 3.5
Answerx = −0.6, y = −2.8 and x = 1.5, y = 3.5
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