Success TutoringWorksheets

Year 10 Simultaneous Equations Worksheet — Level 2 — Answers

Answer sheet with worked solutions for the Year 10 simultaneous equations worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Simultaneous Equations

Year 10 Simultaneous Equations Worksheet — Level 2 — Answers

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

1.Solve simultaneously: 2x + 4y = −4 and 2x − 2y = −10

Answer: x = −4, y = 1

  1. Subtract equation 2 from equation 1: 6y = 6
  2. y = 1
  3. Substitute into equation 1: 2x + 4 = −4, so x = −4
2.Solve simultaneously: 3x + 4y = 46 and 3x − 3y = −3

Answer: x = 6, y = 7

  1. Subtract equation 2 from equation 1: 7y = 49
  2. y = 7
  3. Substitute into equation 1: 3x + 28 = 46, so x = 6
3.Solve simultaneously: 4x + 2y = 24 and 4x − 3y = 44

Answer: x = 8, y = −4

  1. Subtract equation 2 from equation 1: 5y = −20
  2. y = −4
  3. Substitute into equation 1: 4x − 8 = 24, so x = 8
4.Solve simultaneously: 3x + y = −20 and 3x − 4y = 5

Answer: x = −5, y = −5

  1. Subtract equation 2 from equation 1: 5y = −25
  2. y = −5
  3. Substitute into equation 1: 3x − 5 = −20, so x = −5
5.Solve simultaneously: 2x + 3y = −13 and 2x − 2y = 12

Answer: x = 1, y = −5

  1. Subtract equation 2 from equation 1: 5y = −25
  2. y = −5
  3. Substitute into equation 1: 2x − 15 = −13, so x = 1
6.Solve simultaneously: 2x + y = 3 and 2x − 2y = 18

Answer: x = 4, y = −5

  1. Subtract equation 2 from equation 1: 3y = −15
  2. y = −5
  3. Substitute into equation 1: 2x − 5 = 3, so x = 4
7.Solve simultaneously: 2x + 2y = 4 and 2x − 3y = 34

Answer: x = 8, y = −6

  1. Subtract equation 2 from equation 1: 5y = −30
  2. y = −6
  3. Substitute into equation 1: 2x − 12 = 4, so x = 8
8.Solve simultaneously: 3x + y = 14 and 3x − 3y = 6

Answer: x = 4, y = 2

  1. Subtract equation 2 from equation 1: 4y = 8
  2. y = 2
  3. Substitute into equation 1: 3x + 2 = 14, so x = 4
Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Marking tips

  • Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
  • For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
  • Celebrate what went well first, then pick one thing to work on next.

Great work. Here's what to try next: