4MA1/2H Jun 2021, Question 19: 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 = 3 − 2x and x² + y² = 18, showing clear algebraic working.
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Solution · 5 marks
- 1Substitute: x² + (3 − 2x)² = 18
- 2x² + 9 − 12x + 4x² = 18
- 35x² − 12x − 9 = 0
- 4(5x + 3)(x − 3) = 0, so x = 3 or x = −0.6
- 5x = 3: y = 3 − 6 = −3
- 6x = −0.6: y = 3 + 1.2 = 4.2
Answerx = 3, y = −3 and x = −0.6, y = 4.2
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