4MA1/2H Jan 2023, 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 simultaneous equations y = 7 − 2x and x² + y² = 34, showing clear algebraic working.
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Solution · 5 marks
- 1Substitute y = 7 − 2x: x² + (7 − 2x)² = 34
- 2x² + 49 − 28x + 4x² = 34, so 5x² − 28x + 15 = 0
- 3(5x − 3)(x − 5) = 0, so x = 0.6 or x = 5
- 4y = 7 − 2(0.6) = 5.8 and y = 7 − 2(5) = −3
- 5x = 0.6, y = 5.8 and x = 5, y = −3
Answerx = 0.6, y = 5.8 and x = 5, y = −3
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