0580/42 Oct/Nov 2025, Question 19: Simultaneous Equations with a Curve
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 6 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Solve the simultaneous equations y = 5 − 2x and y = 3x² − 7x − 6, showing all working and giving answers to 2 decimal places.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 6 marks
- 13x² − 7x − 6 = 5 − 2x
- 23x² − 5x − 11 = 0
- 3x = [5 ± √((−5)² − 4 × 3 × (−11))]/(2 × 3) = (5 ± √157)/6
- 4x = 2.921… or x = −1.255…
- 5y = 5 − 2(2.921…) = −0.843… and y = 5 − 2(−1.255…) = 7.510…
- 6x = 2.92, y = −0.84 and x = −1.25, y = 7.51
Answerx = 2.92, y = −0.84 and x = −1.25, y = 7.51
Stuck on a step? Read the free lesson: Simultaneous Equations with a Curve
Practise more simultaneous equations with a curve questions
Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on simultaneous equations with a curve
Also searched as: 0580/42/O/N/25 · 0580_w25_qp_42 · 0580 w25 42 · question 19.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.