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4024/21 May/Jun 2020, Question 3: Simultaneous Equations by Elimination

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 8 marks

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The question, in short

Three algebra tasks: rearrange a formula for n, solve a pair of simultaneous equations showing working, and solve a quadratic equation to 2 decimal places with working.

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

Part (a) · 2 marks

Rearrange m = 4n − 3 so that n is the subject.

  1. 1m + 3 = 4n
  2. 2n = (m + 3)/4

Answer(m + 3)/4

Part (b) · 3 marks

Solve the simultaneous equations 10x + 7y = −3 and 5x − y = 3, showing your working.

  1. 15x − y = 3, so 35x − 7y = 21
  2. 2Add to 10x + 7y = −3: 45x = 18
  3. 3x = 0.4
  4. 4y = 5 × 0.4 − 3 = −1
  5. 5x = 0.4, y = −1

Answerx = 0.4, y = −1

Part (c) · 3 marks

Solve 5x² + 3x − 1 = 0, showing all working, giving answers correct to 2 decimal places.

  1. 1x = (−3 ± √(3² − 4 × 5 × (−1)))/(2 × 5)
  2. 2= (−3 ± √29)/10
  3. 3x = (−3 + 5.385…)/10 = 0.2385… or x = (−3 − 5.385…)/10 = −0.8385…
  4. 4x = 0.24 or x = −0.84

Answer0.24, −0.84

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

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