4MA1/2HR Jan 2022, Question 18: 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 2y = x + 1 and 3y² + 7y + 16 = x² − x to find the coordinates of the two intersection points A and B, showing algebraic working.
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Solution · 5 marks
- 1From the line, x = 2y − 1
- 2Substitute: 3y² + 7y + 16 = (2y − 1)² − (2y − 1) = 4y² − 6y + 2
- 3Rearrange: y² − 13y − 14 = 0, so (y − 14)(y + 1) = 0
- 4y = 14 gives x = 2 × 14 − 1 = 27; y = −1 gives x = −3
- 5A and B are (27, 14) and (−3, −1)
Answer(27, 14) and (−3, −1)
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