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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: 4x + 3y = 40 and 3x − 5y = 1

Answer: x = 7, y = 4

  1. Multiply equation 1 by 3 and equation 2 by 4 to match the x coefficients
  2. 12x + 9y = 120 and 12x − 20y = 4
  3. Subtract: 29y = 116, so y = 4
  4. Substitute back: x = 7
2.Solve simultaneously: 2x − y = 20 and 4x + 3y = 20

Answer: x = 8, y = −4

  1. Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
  2. 8x − 4y = 80 and 8x + 6y = 40
  3. Subtract: −10y = 40, so y = −4
  4. Substitute back: x = 8
3.Solve simultaneously: 2x + 4y = 12 and 4x − 4y = −36

Answer: x = −4, y = 5

  1. Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
  2. 8x + 16y = 48 and 8x − 8y = −72
  3. Subtract: 24y = 120, so y = 5
  4. Substitute back: x = −4
4.Solve simultaneously: 2x + 2y = 6 and 5x + 3y = −1

Answer: x = −5, y = 8

  1. Multiply equation 1 by 5 and equation 2 by 2 to match the x coefficients
  2. 10x + 10y = 30 and 10x + 6y = −2
  3. Subtract: 4y = 32, so y = 8
  4. Substitute back: x = −5
5.Solve simultaneously: 3x − 3y = −6 and 3x + 5y = −38

Answer: x = −6, y = −4

  1. Subtract equation 2 from equation 1: −8y = 32
  2. y = −4
  3. Substitute into equation 1: 3x + 12 = −6, so x = −6
6.Solve simultaneously: 2x + 3y = 5 and 3x − 5y = 17

Answer: x = 4, y = −1

  1. Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
  2. 6x + 9y = 15 and 6x − 10y = 34
  3. Subtract: 19y = −19, so y = −1
  4. Substitute back: x = 4
7.Solve simultaneously: 3x + y = −16 and 2x + 5y = −15

Answer: x = −5, y = −1

  1. Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
  2. 6x + 2y = −32 and 6x + 15y = −45
  3. Subtract: −13y = 13, so y = −1
  4. Substitute back: x = −5
8.Solve simultaneously: 2x + y = 5 and 4x − 3y = −5

Answer: x = 1, y = 3

  1. Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
  2. 8x + 4y = 20 and 8x − 6y = −10
  3. Subtract: 10y = 30, so y = 3
  4. Substitute back: x = 1
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