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Year 10 Simultaneous Equations Worksheet — Level 3 — Practice Set 3 — Answers

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Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Simultaneous Equations

Year 10 Simultaneous Equations Worksheet — Level 3 — Practice Set 3 — Answers

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

1.Solve simultaneously: 2x − 2y = −4 and 2x − y = 3

Answer: x = 5, y = 7

  1. Subtract equation 2 from equation 1: −y = −7
  2. y = 7
  3. Substitute into equation 1: 2x − 14 = −4, so x = 5
2.Solve simultaneously: 4x + 2y = 12 and 3x − 3y = −9

Answer: x = 1, y = 4

  1. Multiply equation 1 by 3 and equation 2 by 4 to match the x coefficients
  2. 12x + 6y = 36 and 12x − 12y = −36
  3. Subtract: 18y = 72, so y = 4
  4. Substitute back: x = 1
3.Solve simultaneously: 3x + 4y = 23 and 4x − 5y = −21

Answer: x = 1, y = 5

  1. Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
  2. 12x + 16y = 92 and 12x − 15y = −63
  3. Subtract: 31y = 155, so y = 5
  4. Substitute back: x = 1
4.Solve simultaneously: 4x + y = −6 and 2x + 4y = 4

Answer: x = −2, y = 2

  1. Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
  2. 8x + 2y = −12 and 8x + 16y = 16
  3. Subtract: −14y = −28, so y = 2
  4. Substitute back: x = −2
5.Solve simultaneously: 4x − 4y = 24 and 5x − 4y = 26

Answer: x = 2, y = −4

  1. Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
  2. 20x − 20y = 120 and 20x − 16y = 104
  3. Subtract: −4y = 16, so y = −4
  4. Substitute back: x = 2
6.Solve simultaneously: 3x + 4y = 12 and 2x − y = −14

Answer: x = −4, y = 6

  1. Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
  2. 6x + 8y = 24 and 6x − 3y = −42
  3. Subtract: 11y = 66, so y = 6
  4. Substitute back: x = −4
7.Solve simultaneously: 4x + 2y = 2 and 4x + 4y = 0

Answer: x = 1, y = −1

  1. Subtract equation 2 from equation 1: −2y = 2
  2. y = −1
  3. Substitute into equation 1: 4x − 2 = 2, so x = 1
8.Solve simultaneously: 4x + y = −15 and 5x − 4y = −24

Answer: x = −4, y = 1

  1. Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
  2. 20x + 5y = −75 and 20x − 16y = −96
  3. Subtract: 21y = 21, so y = 1
  4. Substitute back: x = −4
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