0580/12 Oct/Nov 2025, Question 23: Simultaneous Equations by Elimination
Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Non-calculator · 6 marks
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The question, in short
Given bridge tolls a for cars and b for other vehicles, use Monday's 4 cars and 20 others totalling $130 and Tuesday's 6 cars and 15 others totalling $105 to form two equations, then solve for a and b.
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Solution · 6 marks
- 14a + 20b = 130 and 6a + 15b = 105
- 2× 3 and × 2: 12a + 60b = 390 and 12a + 30b = 210
- 3Subtract: 30b = 180, so b = 6
- 44a + 120 = 130, so a = 2.5
- 5a = 2.5, b = 6
Answera = 2.5, b = 6
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