4MA1/1H Jan 2022, Question 19: Simultaneous Equations with a Curve
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
Solve the simultaneous equations 3x² + y² − xy = 5 and y = 2x − 3, showing clear algebraic working.
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Solution · 5 marks
- 1Substitute y = 2x − 3: 3x² + (2x − 3)² − x(2x − 3) = 5
- 2Expand: 3x² + 4x² − 12x + 9 − 2x² + 3x = 5
- 3Simplify: 5x² − 9x + 4 = 0, so (5x − 4)(x − 1) = 0
- 4x = 0.8 gives y = 2(0.8) − 3 = −1.4; x = 1 gives y = −1
- 5x = 0.8 and y = −1.4; x = 1 and y = −1
Answerx = 0.8 and y = −1.4; x = 1 and y = −1
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