Lemmara logoLemmaraWorked solution

0580/32 May/Jun 2024, Question 2: Simultaneous Equations by Elimination

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

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Simplify algebraic expressions, evaluate c² + d² for c = 7 and d = −5, rearrange T = 35m + 20, find a mass from a cooking time, and solve two simultaneous equations showing working.

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

Part (ai) · 1 mark

Simplify 5a − 6a + 3a.

  1. 15a − 6a + 3a = 2a

Answer2a

Part (aii) · 2 marks

Simplify 6x² − 6x − 4x² − x by collecting like terms.

  1. 16x² − 4x² = 2x² and −6x − x = −7x
  2. 2= 2x² − 7x

Answer2x² − 7x

Part (b) · 2 marks

Work out c² + d² given c = 7 and d = −5.

  1. 17² + (−5)² = 49 + 25
  2. 2= 74

Answer74

Part (ci) · 2 marks

Rearrange T = 35m + 20 to make m the subject.

  1. 1T − 20 = 35m
  2. 2m = (T − 20)/35

Answer(T − 20)/35

Part (cii) · 2 marks

Find the mass m of a chicken whose cooking time T is 83 minutes.

  1. 1m = (83 − 20)/35 = 63/35
  2. 2= 1.8 kg

Answer1.8

Part (d) · 3 marks

Solve 5x − 6y = 24 and 15x + 8y = 33 simultaneously, showing all working.

  1. 1First equation × 3: 15x − 18y = 72
  2. 2Subtract from 15x + 8y = 33: 26y = −39
  3. 3y = −1.5
  4. 45x − 6(−1.5) = 24 → 5x = 15 → x = 3
  5. 5x = 3, y = −1.5

Answerx = 3, y = −1.5

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

Practise more simultaneous equations by elimination questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on simultaneous equations by elimination

Also searched as: 0580/32/M/J/24 · 0580_s24_qp_32 · 0580 s24 32 · question 2.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.