4MA1/2H Jun 2023, Question 21: 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 2x² + 3y² = 11 and x = 3y − 1, showing clear algebraic working.
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Solution · 5 marks
- 1Substitute x = 3y − 1: 2(3y − 1)² + 3y² = 11
- 2Expand: 18y² − 12y + 2 + 3y² = 11, so 21y² − 12y − 9 = 0
- 3Divide by 3 and factorise: (7y + 3)(y − 1) = 0, so y = 1 or y = −3/7
- 4x = 3y − 1 gives x = 2 or x = −16/7
- 5x = 2, y = 1 and x = −16/7, y = −3/7
Answerx = 2, y = 1 and x = −16/7, y = −3/7
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