4MA1/2HR Jun 2022, Question 21: 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 x − 2y = 3 and x² − y² + 2x = 10, showing clear algebraic working.
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Solution · 5 marks
- 1x = 3 + 2y
- 2(3 + 2y)² − y² + 2(3 + 2y) = 10
- 39 + 12y + 4y² − y² + 6 + 4y = 10
- 43y² + 16y + 5 = 0
- 5(3y + 1)(y + 5) = 0
- 6y = −1/3 or y = −5
- 7x = 3 + 2(−1/3) = 3 − 2/3 = 7/3
- 8x = 3 + 2(−5) = 3 − 10 = −7
- 9x = 7/3, y = −1/3; x = −7, y = −5
Answerx = 7/3, y = −1/3; x = −7, y = −5
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