4MA1/1HR Jun 2019, Question 22: Simultaneous Equations with a Curve
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
Solve the simultaneous equations 2x² + 3y² = 5 and y = 2x + 1, showing clear algebraic working.
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Solution · 5 marks
- 1Substitute y = 2x + 1: 2x² + 3(2x + 1)² = 5
- 22x² + 12x² + 12x + 3 = 5, so 7x² + 6x − 1 = 0
- 3(7x − 1)(x + 1) = 0, so x = 1/7 or x = −1
- 4x = −1 gives y = −1; x = 1/7 gives y = 9/7
- 5x = −1, y = −1 and x = 1/7, y = 9/7
Answerx = −1, y = −1 and x = 1/7, y = 9/7
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