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

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Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Simultaneous Equations

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

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

1.Solve simultaneously: 3x + 4y = 18 and 3x − 3y = −3

Answer: x = 2, y = 3

  1. Subtract equation 2 from equation 1: 7y = 21
  2. y = 3
  3. Substitute into equation 1: 3x + 12 = 18, so x = 2
2.Solve simultaneously: 4x + 4y = 40 and 4x − 5y = −32

Answer: x = 2, y = 8

  1. Subtract equation 2 from equation 1: 9y = 72
  2. y = 8
  3. Substitute into equation 1: 4x + 32 = 40, so x = 2
3.Solve simultaneously: 4x + y = −30 and 4x − 2y = −12

Answer: x = −6, y = −6

  1. Subtract equation 2 from equation 1: 3y = −18
  2. y = −6
  3. Substitute into equation 1: 4x − 6 = −30, so x = −6
4.Solve simultaneously: 2x + 3y = 2 and 2x − 2y = −18

Answer: x = −5, y = 4

  1. Subtract equation 2 from equation 1: 5y = 20
  2. y = 4
  3. Substitute into equation 1: 2x + 12 = 2, so x = −5
5.Solve simultaneously: 4x + 2y = 6 and 4x − 3y = 11

Answer: x = 2, y = −1

  1. Subtract equation 2 from equation 1: 5y = −5
  2. y = −1
  3. Substitute into equation 1: 4x − 2 = 6, so x = 2
6.Solve simultaneously: 3x + y = 19 and 3x − 2y = 16

Answer: x = 6, y = 1

  1. Subtract equation 2 from equation 1: 3y = 3
  2. y = 1
  3. Substitute into equation 1: 3x + 1 = 19, so x = 6
7.Solve simultaneously: 3x + 4y = 40 and 3x − 2y = −2

Answer: x = 4, y = 7

  1. Subtract equation 2 from equation 1: 6y = 42
  2. y = 7
  3. Substitute into equation 1: 3x + 28 = 40, so x = 4
8.Solve simultaneously: 4x + y = −1 and 4x − 3y = 19

Answer: x = 1, y = −5

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