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Year 10 Simultaneous Equations Worksheet — Level 1 — Answers

Answer sheet with worked solutions for the Year 10 simultaneous equations worksheet.

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Year 10 · Mathematics · Simultaneous Equations

Year 10 Simultaneous Equations Worksheet — Level 1 — Answers

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

1.Solve simultaneously: x + 2y = −1 and x − 3y = 9

Answer: x = 3, y = −2

  1. Subtract equation 2 from equation 1: 5y = −10
  2. y = −2
  3. Substitute into equation 1: x − 4 = −1, so x = 3
2.Solve simultaneously: x + y = 7 and x − y = 1

Answer: x = 4, y = 3

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

Answer: x = 3, y = −3

  1. Subtract equation 2 from equation 1: 5y = −15
  2. y = −3
  3. Substitute into equation 1: x − 6 = −3, so x = 3
4.Solve simultaneously: x + 4y = −6 and x − 2y = 6

Answer: x = 2, y = −2

  1. Subtract equation 2 from equation 1: 6y = −12
  2. y = −2
  3. Substitute into equation 1: x − 8 = −6, so x = 2
5.Solve simultaneously: x + 3y = 18 and x − 4y = −31

Answer: x = −3, y = 7

  1. Subtract equation 2 from equation 1: 7y = 49
  2. y = 7
  3. Substitute into equation 1: x + 21 = 18, so x = −3
6.Solve simultaneously: x + 4y = 23 and x − y = 3

Answer: x = 7, y = 4

  1. Subtract equation 2 from equation 1: 5y = 20
  2. y = 4
  3. Substitute into equation 1: x + 16 = 23, so x = 7
7.Solve simultaneously: x + y = −3 and x − 4y = −13

Answer: x = −5, y = 2

  1. Subtract equation 2 from equation 1: 5y = 10
  2. y = 2
  3. Substitute into equation 1: x + 2 = −3, so x = −5
8.Solve simultaneously: x + y = −3 and x − 3y = 17

Answer: x = 2, y = −5

  1. Subtract equation 2 from equation 1: 4y = −20
  2. y = −5
  3. Substitute into equation 1: x − 5 = −3, so x = 2
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