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0580/33 Oct/Nov 2024, Question 4: Simultaneous Equations by Elimination

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 10 marks

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The question, in short

Four-part algebra question: substitute values into a formula, factorise an expression, write a cost expression, and solve simultaneous equations showing working.

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

Part (a) · 2 marks

Given n = 15r + 20c, find r when n = 180 and c = 3.

  1. 1180 = 15r + 20 × 3
  2. 215r = 120
  3. 3r = 8

Answer8

Part (b) · 2 marks

Factorise 20p²q − 5p completely.

  1. 1Common factor 5p
  2. 220p²q − 5p = 5p(4pq − 1)

Answer5p(4pq − 1)

Part (c) · 2 marks

Apples 35 cents, bananas 14 cents: write an expression in cents for x apples and y bananas.

  1. 1Apples: 35x, bananas: 14y
  2. 235x + 14y

Answer35x + 14y

Part (d) · 4 marks

Solve 8x + 3y = 59 and 5x + 7y = 83, showing all working.

  1. 1× 7: 56x + 21y = 413
  2. 2× 3: 15x + 21y = 249
  3. 3Subtract: 41x = 164, x = 4
  4. 48 × 4 + 3y = 59, 3y = 27, y = 9
  5. 5x = 4, y = 9

Answerx = 4, y = 9

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Also searched as: 0580/33/O/N/24 · 0580_w24_qp_33 · 0580 w24 33 · question 4.
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