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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: 2x + 2y = 22 and 3x − 5y = −23

Answer: x = 4, y = 7

  1. Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
  2. 6x + 6y = 66 and 6x − 10y = −46
  3. Subtract: 16y = 112, so y = 7
  4. Substitute back: x = 4
2.Solve simultaneously: 4x + y = 34 and 5x + 5y = 65

Answer: x = 7, y = 6

  1. Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
  2. 20x + 5y = 170 and 20x + 20y = 260
  3. Subtract: −15y = −90, so y = 6
  4. Substitute back: x = 7
3.Solve simultaneously: 2x + 3y = 38 and 4x + 4y = 60

Answer: x = 7, y = 8

  1. Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
  2. 8x + 12y = 152 and 8x + 8y = 120
  3. Subtract: 4y = 32, so y = 8
  4. Substitute back: x = 7
4.Solve simultaneously: 4x + 2y = −4 and 3x − 3y = −12

Answer: x = −2, y = 2

  1. Multiply equation 1 by 3 and equation 2 by 4 to match the x coefficients
  2. 12x + 6y = −12 and 12x − 12y = −48
  3. Subtract: 18y = 36, so y = 2
  4. Substitute back: x = −2
5.Solve simultaneously: 2x + 3y = 13 and 4x − 5y = −51

Answer: x = −4, y = 7

  1. Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
  2. 8x + 12y = 52 and 8x − 10y = −102
  3. Subtract: 22y = 154, so y = 7
  4. Substitute back: x = −4
6.Solve simultaneously: 2x + 4y = −2 and 4x + 5y = 8

Answer: x = 7, y = −4

  1. Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
  2. 8x + 16y = −8 and 8x + 10y = 16
  3. Subtract: 6y = −24, so y = −4
  4. Substitute back: x = 7
7.Solve simultaneously: 3x − 2y = 33 and 5x + 5y = 5

Answer: x = 7, y = −6

  1. Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
  2. 15x − 10y = 165 and 15x + 15y = 15
  3. Subtract: −25y = 150, so y = −6
  4. Substitute back: x = 7
8.Solve simultaneously: 3x − 4y = −43 and 3x + y = −8

Answer: x = −5, y = 7

  1. Subtract equation 2 from equation 1: −5y = −35
  2. y = 7
  3. Substitute into equation 1: 3x − 28 = −43, so x = −5
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