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0580/32 Oct/Nov 2023, Question 6: Simultaneous Equations by Elimination

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 12 marks

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The question, in short

Simplify algebraic expressions, find a square's side from a pentagon's perimeter, and solve simultaneous equations for tea and cake costs.

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

Part (a) · 1 mark

Simplify a + 4a − 3a.

  1. 1a + 4a − 3a = 2a

Answer2a

Part (b) · 1 mark

Simplify 8b − 4 × 7b.

  1. 14 × 7b = 28b
  2. 28b − 28b = −20b

Answer−20b

Part (c) · 4 marks

Using the pentagon's five side expressions, find an expression for one side of a square with equal perimeter.

  1. 1Perimeter = (4x + 3) + (x + 7) + (9x + 8) + (7x + 3) + (3x − 9) = 24x + 12
  2. 2Side of square = (24x + 12) ÷ 4
  3. 3= 6x + 3

Answer6x + 3

Part (d) · 6 marks

Form and solve simultaneous equations from 5 teas and 4 cakes costing $15.69, and 3 teas and 7 cakes costing $17.97.

  1. 15t + 4c = 15.69 and 3t + 7c = 17.97
  2. 2× 3 and × 5: 15t + 12c = 47.07 and 15t + 35c = 89.85
  3. 3Subtract: 23c = 42.78, c = 1.86
  4. 45t = 15.69 − 4 × 1.86 = 8.25, t = 1.65
  5. 5Tea $1.65, Cake $1.86

AnswerTea $1.65, Cake $1.86

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

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Also searched as: 0580/32/O/N/23 · 0580_w23_qp_32 · 0580 w23 32 · question 6.
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