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Year 12 Simultaneous Equations Worksheet — Level 2 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 12 simultaneous equations worksheet.

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Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Simultaneous Equations

Year 12 Simultaneous Equations Worksheet — Level 2 — Practice Set 3 — Answers

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

1.Solve simultaneously: 2x + 2y = 22 and 2x − 3y = −3

Answer: x = 6, y = 5

  1. Subtract equation 2 from equation 1: 5y = 25
  2. y = 5
  3. Substitute into equation 1: 2x + 10 = 22, so x = 6
2.Solve simultaneously: 2x + 4y = 16 and 2x − 5y = −2

Answer: x = 4, y = 2

  1. Subtract equation 2 from equation 1: 9y = 18
  2. y = 2
  3. Substitute into equation 1: 2x + 8 = 16, so x = 4
3.Solve simultaneously: 4x + y = −12 and 4x − 2y = −36

Answer: x = −5, y = 8

  1. Subtract equation 2 from equation 1: 3y = 24
  2. y = 8
  3. Substitute into equation 1: 4x + 8 = −12, so x = −5
4.Solve simultaneously: 3x + 3y = 0 and 3x − 4y = −35

Answer: x = −5, y = 5

  1. Subtract equation 2 from equation 1: 7y = 35
  2. y = 5
  3. Substitute into equation 1: 3x + 15 = 0, so x = −5
5.Solve simultaneously: 4x + 3y = 9 and 4x − 4y = 16

Answer: x = 3, y = −1

  1. Subtract equation 2 from equation 1: 7y = −7
  2. y = −1
  3. Substitute into equation 1: 4x − 3 = 9, so x = 3
6.Solve simultaneously: 4x + 4y = −4 and 4x − y = 11

Answer: x = 2, y = −3

  1. Subtract equation 2 from equation 1: 5y = −15
  2. y = −3
  3. Substitute into equation 1: 4x − 12 = −4, so x = 2
7.Solve simultaneously: 4x + 3y = 12 and 4x − 4y = 40

Answer: x = 6, y = −4

  1. Subtract equation 2 from equation 1: 7y = −28
  2. y = −4
  3. Substitute into equation 1: 4x − 12 = 12, so x = 6
8.Solve simultaneously: 2x + 3y = −24 and 2x − 2y = 6

Answer: x = −3, y = −6

  1. Subtract equation 2 from equation 1: 5y = −30
  2. y = −6
  3. Substitute into equation 1: 2x − 18 = −24, so x = −3
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