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Year 9 Simultaneous Equations Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 9 simultaneous equations worksheet.

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Simultaneous Equations

Year 9 Simultaneous Equations Worksheet — Level 3 — Answers

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

1.Solve simultaneously: 2x + 2y = 6 and 4x − 5y = 48

Answer: x = 7, y = −4

  1. Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
  2. 8x + 8y = 24 and 8x − 10y = 96
  3. Subtract: 18y = −72, so y = −4
  4. Substitute back: x = 7
2.Solve simultaneously: 3x − 4y = −8 and 5x + 4y = −24

Answer: x = −4, y = −1

  1. Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
  2. 15x − 20y = −40 and 15x + 12y = −72
  3. Subtract: −32y = 32, so y = −1
  4. Substitute back: x = −4
3.Solve simultaneously: 3x − y = 2 and 4x − 4y = 0

Answer: x = 1, y = 1

  1. Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
  2. 12x − 4y = 8 and 12x − 12y = 0
  3. Subtract: 8y = 8, so y = 1
  4. Substitute back: x = 1
4.Solve simultaneously: 4x + y = 28 and 2x − y = 8

Answer: x = 6, y = 4

  1. Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
  2. 8x + 2y = 56 and 8x − 4y = 32
  3. Subtract: 6y = 24, so y = 4
  4. Substitute back: x = 6
5.Solve simultaneously: 4x − 4y = −36 and 3x + 3y = −3

Answer: x = −5, y = 4

  1. Multiply equation 1 by 3 and equation 2 by 4 to match the x coefficients
  2. 12x − 12y = −108 and 12x + 12y = −12
  3. Subtract: −24y = −96, so y = 4
  4. Substitute back: x = −5
6.Solve simultaneously: 3x − 2y = −18 and 4x − 3y = −26

Answer: x = −2, y = 6

  1. Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
  2. 12x − 8y = −72 and 12x − 9y = −78
  3. Subtract: y = 6, so y = 6
  4. Substitute back: x = −2
7.Solve simultaneously: 4x + 4y = 8 and 2x + 3y = −1

Answer: x = 7, y = −5

  1. Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
  2. 8x + 8y = 16 and 8x + 12y = −4
  3. Subtract: −4y = 20, so y = −5
  4. Substitute back: x = 7
8.Solve simultaneously: 4x + 3y = 6 and 4x − y = 14

Answer: x = 3, y = −2

  1. Subtract equation 2 from equation 1: 4y = −8
  2. y = −2
  3. Substitute into equation 1: 4x − 6 = 6, so x = 3
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