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Year 10 Simultaneous Equations Worksheet — Level 3 — Answers

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Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Simultaneous Equations

Year 10 Simultaneous Equations Worksheet — Level 3 — Answers

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

1.Solve simultaneously: 3x + y = −1 and 5x − 2y = −9

Answer: x = −1, y = 2

  1. Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
  2. 15x + 5y = −5 and 15x − 6y = −27
  3. Subtract: 11y = 22, so y = 2
  4. Substitute back: x = −1
2.Solve simultaneously: 2x + 2y = −6 and 5x − 3y = −31

Answer: x = −5, y = 2

  1. Multiply equation 1 by 5 and equation 2 by 2 to match the x coefficients
  2. 10x + 10y = −30 and 10x − 6y = −62
  3. Subtract: 16y = 32, so y = 2
  4. Substitute back: x = −5
3.Solve simultaneously: 4x − 3y = −2 and 5x − 4y = −2

Answer: x = −2, y = −2

  1. Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
  2. 20x − 15y = −10 and 20x − 16y = −8
  3. Subtract: y = −2, so y = −2
  4. Substitute back: x = −2
4.Solve simultaneously: 4x + 4y = −36 and 4x − 3y = −1

Answer: x = −4, y = −5

  1. Subtract equation 2 from equation 1: 7y = −35
  2. y = −5
  3. Substitute into equation 1: 4x − 20 = −36, so x = −4
5.Solve simultaneously: 4x + 3y = −6 and 2x − 4y = −36

Answer: x = −6, y = 6

  1. Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
  2. 8x + 6y = −12 and 8x − 16y = −144
  3. Subtract: 22y = 132, so y = 6
  4. Substitute back: x = −6
6.Solve simultaneously: 2x − 4y = −22 and 4x − y = 5

Answer: x = 3, y = 7

  1. Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
  2. 8x − 16y = −88 and 8x − 2y = 10
  3. Subtract: −14y = −98, so y = 7
  4. Substitute back: x = 3
7.Solve simultaneously: 3x + y = 10 and 5x − y = 6

Answer: x = 2, y = 4

  1. Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
  2. 15x + 5y = 50 and 15x − 3y = 18
  3. Subtract: 8y = 32, so y = 4
  4. Substitute back: x = 2
8.Solve simultaneously: 2x + 2y = 6 and 3x − 5y = −31

Answer: x = −2, y = 5

  1. Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
  2. 6x + 6y = 18 and 6x − 10y = −62
  3. Subtract: 16y = 80, so y = 5
  4. Substitute back: x = −2
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