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Year 9 Simultaneous Equations Worksheet — Level 3 — Practice Set 3 — Answers

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Simultaneous Equations

Year 9 Simultaneous Equations Worksheet — Level 3 — Practice Set 3 — Answers

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

1.Solve simultaneously: 3x − 3y = −36 and 3x + 3y = 6

Answer: x = −5, y = 7

  1. Subtract equation 2 from equation 1: −6y = −42
  2. y = 7
  3. Substitute into equation 1: 3x − 21 = −36, so x = −5
2.Solve simultaneously: 3x − 4y = 20 and 3x + 3y = 6

Answer: x = 4, y = −2

  1. Subtract equation 2 from equation 1: −7y = 14
  2. y = −2
  3. Substitute into equation 1: 3x + 8 = 20, so x = 4
3.Solve simultaneously: 2x + 3y = 11 and 2x − 4y = −24

Answer: x = −2, y = 5

  1. Subtract equation 2 from equation 1: 7y = 35
  2. y = 5
  3. Substitute into equation 1: 2x + 15 = 11, so x = −2
4.Solve simultaneously: 2x + 2y = −14 and 5x − 5y = −5

Answer: x = −4, y = −3

  1. Multiply equation 1 by 5 and equation 2 by 2 to match the x coefficients
  2. 10x + 10y = −70 and 10x − 10y = −10
  3. Subtract: 20y = −60, so y = −3
  4. Substitute back: x = −4
5.Solve simultaneously: 4x + 3y = 14 and 5x − 3y = 31

Answer: x = 5, y = −2

  1. Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
  2. 20x + 15y = 70 and 20x − 12y = 124
  3. Subtract: 27y = −54, so y = −2
  4. Substitute back: x = 5
6.Solve simultaneously: 2x + y = −8 and 2x + 5y = −32

Answer: x = −1, y = −6

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

Answer: x = −3, y = −5

  1. Multiply equation 1 by 5 and equation 2 by 2 to match the x coefficients
  2. 10x − 10y = 20 and 10x − 8y = 10
  3. Subtract: −2y = 10, so y = −5
  4. Substitute back: x = −3
8.Solve simultaneously: 2x − 3y = −5 and 2x + 5y = −13

Answer: x = −4, y = −1

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