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4024/12 May/Jun 2025, Question 11: Simultaneous Equations by Elimination

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

Small box mass x kg, large box y kg. Use given totals to form equations, then solve simultaneous equations to find both masses, showing working.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

Given 4 small and 6 large boxes total 30 kg, show that 2x + 3y = 15.

  1. 14x + 6y = 30
  2. 2Divide by 2: 2x + 3y = 15

Answer4x + 6y = 30 leading to 2x + 3y = 15 with no errors

Part (b) · 1 mark

Given 6 small boxes and 1 large box total 13 kg, write an equation in x and y.

  1. 16x + y = 13

Answer6x + y = 13

Part (c) · 3 marks

Solve 2x + 3y = 15 and 6x + y = 13 to find the mass of each box type, showing all working.

  1. 1Multiply 6x + y = 13 by 3: 18x + 3y = 39
  2. 2Subtract 2x + 3y = 15: 16x = 24, so x = 1.5
  3. 3y = 13 − 6 × 1.5 = 4
  4. 4Small box = 1.5 kg, large box = 4 kg

AnswerSmall box = 1.5, Large box = 4

Stuck on a step? Read the free lesson: Simultaneous Equations by Elimination

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