4MA1/2HR Jun 2018, Question 18: 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 2x² + 3y² = 14 and x = 2y − 3, showing clear algebraic working.
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Solution · 5 marks
- 1Substitute: 2(2y − 3)² + 3y² = 14
- 22(4y² − 12y + 9) + 3y² = 14
- 311y² − 24y + 4 = 0
- 4(11y − 2)(y − 2) = 0, so y = 2 or y = 2/11
- 5y = 2: x = 4 − 3 = 1
- 6y = 2/11: x = 4/11 − 3 = −29/11
Answerx = 1, y = 2 and x = −29/11, y = 2/11
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