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0580/33 Oct/Nov 2021, Question 9: Simultaneous Equations by Elimination

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

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The question, in short

Students simplify an algebraic expression, solve a linear equation, find an index value, and form and solve simultaneous equations for calculator and pen prices.

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Part (a) · 1 mark

Combine the like terms in 3g + 7g − 4g to give a single term.

  1. 13g + 7g − 4g = 6g

Answer6g

Part (b) · 2 marks

Find the value of x that satisfies 4x + 5 = 27.

  1. 14x = 27 − 5 = 22
  2. 2x = 5.5

Answer5.5

Part (c) · 1 mark

Given 6ᵖ × 6³ = 6¹⁷, determine the number p.

  1. 1p + 3 = 17
  2. 2p = 14

Answer14

Part (d) · 6 marks

Using Mia's 4 calculators and 2 pens for $20.60 and Heidi's 5 calculators and 3 pens for $26.90, set up two equations and solve for each item's cost.

  1. 14c + 2p = 20.60 and 5c + 3p = 26.90
  2. 2×3: 12c + 6p = 61.80; ×2: 10c + 6p = 53.80
  3. 3Subtract: 2c = 8, c = 4
  4. 44 × 4 + 2p = 20.60, 2p = 4.60, p = 2.30
  5. 5Calculator $4, pen $2.30

AnswerCalculator $4, Pen $2.30

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Also searched as: 0580/33/O/N/21 · 0580_w21_qp_33 · 0580 w21 33 · question 9.
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