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4MA1/2HR Jan 2020, Question 19: Solving Linear Equations

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

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The question, in short

Solve an equation in x involving two algebraic fractions and show working, then solve a quadratic inequality in y.

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

Part (a) · 3 marks

Solve (4 − 3x)/5 − (3x − 5)/2 = −3, showing clear algebraic working.

  1. 1(4 − 3x)/5 − (3x − 5)/2 = −3
  2. 2Multiply every term by 10: 2(4 − 3x) − 5(3x − 5) = −30
  3. 3Expand the brackets: 8 − 6x − 15x + 25 = −30
  4. 4Collect like terms: 33 − 21x = −30
  5. 5−21x = −30 − 33
  6. 6−21x = −63
  7. 7x = 3

Answerx = 3

Part (b) · 3 marks

Solve the inequality 5y² − 17y ≤ 40.

  1. 15y² − 17y ≤ 40
  2. 25y² − 17y − 40 ≤ 0
  3. 3Factorise: (5y + 8)(y − 5) ≤ 0
  4. 4The critical values are y = −8/5 = −1.6 and y = 5
  5. 5The graph of y = 5y² − 17y − 40 is a positive parabola, so it is below the axis between the critical values
  6. 6−1.6 ≤ y ≤ 5

Answer−1.6 ≤ y ≤ 5

Stuck on a step? Read the free lesson: Solving Linear Equations

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