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Mathematics · Topic

Linear and simultaneous equations

One mark usually belongs to the method, so write the elimination or substitution step.

2 original questions in the bank, worth 6 marks · above the two-per-topic floor

Drill this topic All linear and simultaneous equations questions

The questions, with the examiner reasoning

Solve3 marksBGCSE

Solve the simultaneous equations: 3x + 2y = 16 and x − y = 2, showing your method.

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Answer: x = 4, y = 2

  1. From the second equation: x = y + 2
  2. Substitute: 3(y + 2) + 2y = 16
  3. Expand: 5y + 6 = 16, so y = 2 and x = 4

Examiner technique: Substitution is quicker than elimination when one equation already says x = something. Marks are given for the substitution step, so write it before you solve.

Solve3 marksIGCSE

Solve 3(2x − 1) = 2(x + 4) + 5.

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Answer: x = 4

  1. Expand both sides: 6x − 3 = 2x + 8 + 5
  2. Simplify the right: 6x − 3 = 2x + 13
  3. Collect: 4x = 16, so x = 4

Examiner technique: Expand both sides first, then collect. Collecting before expanding is where sign errors are born.