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Year 10 Simultaneous Equations Worksheet — Level 2 — Answers

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Year 10 · Mathematics · Simultaneous Equations

Year 10 Simultaneous Equations Worksheet — Level 2 — Answers

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Solve each pair of equations. Check your solution satisfies both equations.

1.Solve simultaneously: 4x + 3y = 36 and 4x − 4y = 8

Answer: x = 6, y = 4

  1. Subtract equation 2 from equation 1: 7y = 28
  2. y = 4
  3. Substitute into equation 1: 4x + 12 = 36, so x = 6
2.Solve simultaneously: 3x + 2y = 8 and 3x − 3y = 3

Answer: x = 2, y = 1

  1. Subtract equation 2 from equation 1: 5y = 5
  2. y = 1
  3. Substitute into equation 1: 3x + 2 = 8, so x = 2
3.Solve simultaneously: 2x + y = 9 and 2x − 2y = 6

Answer: x = 4, y = 1

  1. Subtract equation 2 from equation 1: 3y = 3
  2. y = 1
  3. Substitute into equation 1: 2x + 1 = 9, so x = 4
4.Solve simultaneously: 4x + y = −16 and 4x − 4y = −56

Answer: x = −6, y = 8

  1. Subtract equation 2 from equation 1: 5y = 40
  2. y = 8
  3. Substitute into equation 1: 4x + 8 = −16, so x = −6
5.Solve simultaneously: 3x + 4y = −7 and 3x − 3y = 21

Answer: x = 3, y = −4

  1. Subtract equation 2 from equation 1: 7y = −28
  2. y = −4
  3. Substitute into equation 1: 3x − 16 = −7, so x = 3
6.Solve simultaneously: 4x + 3y = 48 and 4x − 2y = 8

Answer: x = 6, y = 8

  1. Subtract equation 2 from equation 1: 5y = 40
  2. y = 8
  3. Substitute into equation 1: 4x + 24 = 48, so x = 6
7.Solve simultaneously: 4x + 3y = 33 and 4x − 4y = −16

Answer: x = 3, y = 7

  1. Subtract equation 2 from equation 1: 7y = 49
  2. y = 7
  3. Substitute into equation 1: 4x + 21 = 33, so x = 3
8.Solve simultaneously: 2x + 3y = 32 and 2x − 2y = −8

Answer: x = 4, y = 8

  1. Subtract equation 2 from equation 1: 5y = 40
  2. y = 8
  3. Substitute into equation 1: 2x + 24 = 32, so x = 4
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