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Year 9 Simultaneous Equations Worksheet — Level 3 — Practice Set 2 — Answers

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Simultaneous Equations

Year 9 Simultaneous Equations Worksheet — Level 3 — Practice Set 2 — Answers

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

1.Solve simultaneously: 3x + 3y = 27 and 2x + y = 12

Answer: x = 3, y = 6

  1. Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
  2. 6x + 6y = 54 and 6x + 3y = 36
  3. Subtract: 3y = 18, so y = 6
  4. Substitute back: x = 3
2.Solve simultaneously: 2x − 2y = 16 and 2x − 3y = 19

Answer: x = 5, y = −3

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

Answer: x = −3, y = −2

  1. Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
  2. 12x − 16y = −4 and 12x − 3y = −30
  3. Subtract: −13y = 26, so y = −2
  4. Substitute back: x = −3
4.Solve simultaneously: 2x + 4y = 22 and 5x + y = 28

Answer: x = 5, y = 3

  1. Multiply equation 1 by 5 and equation 2 by 2 to match the x coefficients
  2. 10x + 20y = 110 and 10x + 2y = 56
  3. Subtract: 18y = 54, so y = 3
  4. Substitute back: x = 5
5.Solve simultaneously: 2x + 3y = 3 and 5x − 4y = −50

Answer: x = −6, y = 5

  1. Multiply equation 1 by 5 and equation 2 by 2 to match the x coefficients
  2. 10x + 15y = 15 and 10x − 8y = −100
  3. Subtract: 23y = 115, so y = 5
  4. Substitute back: x = −6
6.Solve simultaneously: 4x − 4y = 0 and 5x − 3y = 12

Answer: x = 6, y = 6

  1. Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
  2. 20x − 20y = 0 and 20x − 12y = 48
  3. Subtract: −8y = −48, so y = 6
  4. Substitute back: x = 6
7.Solve simultaneously: 3x + y = 13 and 4x − 5y = 49

Answer: x = 6, y = −5

  1. Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
  2. 12x + 4y = 52 and 12x − 15y = 147
  3. Subtract: 19y = −95, so y = −5
  4. Substitute back: x = 6
8.Solve simultaneously: 3x + 3y = 0 and 2x + 3y = −2

Answer: x = 2, y = −2

  1. Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
  2. 6x + 6y = 0 and 6x + 9y = −6
  3. Subtract: −3y = 6, so y = −2
  4. Substitute back: x = 2
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