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4MA1/2F Jun 2020, Question 21: Simultaneous Equations by Elimination

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2F (Foundation) · Calculator · 6 marks

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The question, in short

Simplify two index expressions, then solve a pair of simultaneous equations in x and y, showing algebraic working.

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

Part (a) · 1 mark

Simplify g⁶ × g⁴ by combining the powers of g.

  1. 1When multiplying, add the powers
  2. 2g⁶ × g⁴ = g⁶⁺⁴ = g¹⁰

Answerg¹⁰

Part (b) · 2 marks

Simplify (3cd⁴)², applying the square to the coefficient and the powers.

  1. 1Square each part: 3² × c² × (d⁴)²
  2. 23² = 9 and (d⁴)² = d⁸ (multiply the powers 4 × 2).
  3. 3Answer: 9c²d⁸

Answer9c²d⁸

Part (c) · 3 marks

Solve 4x + 3y = 17 and x + 2y = 5 simultaneously, showing clear algebraic working.

  1. 1Multiply x + 2y = 5 by 4: 4x + 8y = 20
  2. 2Subtract 4x + 3y = 17: 5y = 3, so y = 0.6
  3. 3x + 2 × 0.6 = 5, so x = 5 − 1.2 = 3.8
  4. 4x = 3.8, y = 0.6

Answerx = 3.8, y = 0.6

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

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