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4MA1/1FR Jun 2023, Question 28: Simultaneous Equations by Elimination

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1FR (Foundation) · Calculator · 5 marks

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The question, in short

For a biased 6-sided dice with probabilities x, 0.15, 0.5, y, 0.13, 0.03, show a sum relation and solve simultaneous equations for x and y.

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Part (a) · 2 marks

Use the fact that all six probabilities sum to 1 to show that x + y = 0.19.

  1. 1x + 0.15 + 0.5 + y + 0.13 + 0.03 = 1
  2. 2x + y + 0.81 = 1
  3. 3x + y = 1 − 0.81
  4. 4x + y = 0.19

Answerx + y = 0.19

Part (b) · 3 marks

Solve the simultaneous equations 3x − y = 0.09 and x + y = 0.19 to find x and y, showing algebraic working.

  1. 1x + y = 0.19
  2. 23x − y = 0.09
  3. 3Add the equations: (x + 3x) + (y − y) = 0.19 + 0.09
  4. 44x = 0.28
  5. 5x = 0.28 / 4
  6. 6x = 0.07
  7. 7Substitute x = 0.07 into x + y = 0.19
  8. 80.07 + y = 0.19
  9. 9y = 0.19 − 0.07
  10. 10y = 0.12

Answerx = 0.07 and y = 0.12

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