4MA1/1HR Jan 2021, Question 17: 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 x − 6y = 5 and xy − 2y² = 6, showing clear algebraic working.
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Solution · 5 marks
- 1Rearrange the first equation: x = 6y + 5
- 2Substitute: (6y + 5)y − 2y² = 6, so 4y² + 5y − 6 = 0
- 3Factorise: (4y − 3)(y + 2) = 0, so y = 3/4 or y = −2
- 4Use x = 6y + 5: y = 3/4 gives x = 19/2, y = −2 gives x = −7
- 5x = 19/2, y = 3/4; x = −7, y = −2
Answerx = 19/2, y = 3/4; x = −7, y = −2
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