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Year 12 Simultaneous Equations Worksheet — Level 2 — Practice Set 4 — Answers

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Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Simultaneous Equations

Year 12 Simultaneous Equations Worksheet — Level 2 — Practice Set 4 — Answers

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

1.Solve simultaneously: 4x + 4y = 20 and 4x − 5y = −7

Answer: x = 2, y = 3

  1. Subtract equation 2 from equation 1: 9y = 27
  2. y = 3
  3. Substitute into equation 1: 4x + 12 = 20, so x = 2
2.Solve simultaneously: 4x + 2y = −4 and 4x − 3y = 26

Answer: x = 2, y = −6

  1. Subtract equation 2 from equation 1: 5y = −30
  2. y = −6
  3. Substitute into equation 1: 4x − 12 = −4, so x = 2
3.Solve simultaneously: 3x + 2y = −12 and 3x − 3y = −27

Answer: x = −6, y = 3

  1. Subtract equation 2 from equation 1: 5y = 15
  2. y = 3
  3. Substitute into equation 1: 3x + 6 = −12, so x = −6
4.Solve simultaneously: 2x + y = 1 and 2x − 3y = −27

Answer: x = −3, y = 7

  1. Subtract equation 2 from equation 1: 4y = 28
  2. y = 7
  3. Substitute into equation 1: 2x + 7 = 1, so x = −3
5.Solve simultaneously: 3x + 4y = 47 and 3x − 2y = −1

Answer: x = 5, y = 8

  1. Subtract equation 2 from equation 1: 6y = 48
  2. y = 8
  3. Substitute into equation 1: 3x + 32 = 47, so x = 5
6.Solve simultaneously: 3x + 4y = −30 and 3x − 5y = 24

Answer: x = −2, y = −6

  1. Subtract equation 2 from equation 1: 9y = −54
  2. y = −6
  3. Substitute into equation 1: 3x − 24 = −30, so x = −2
7.Solve simultaneously: 3x + y = −11 and 3x − 3y = −27

Answer: x = −5, y = 4

  1. Subtract equation 2 from equation 1: 4y = 16
  2. y = 4
  3. Substitute into equation 1: 3x + 4 = −11, so x = −5
8.Solve simultaneously: 2x + 4y = 6 and 2x − 5y = 15

Answer: x = 5, y = −1

  1. Subtract equation 2 from equation 1: 9y = −9
  2. y = −1
  3. Substitute into equation 1: 2x − 4 = 6, so x = 5
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