Success TutoringWorksheets

Year 11 Simultaneous Equations Worksheet — Level 2 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 11 simultaneous equations worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Simultaneous Equations

Year 11 Simultaneous Equations Worksheet — Level 2 — Practice Set 3 — Answers

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

1.Solve simultaneously: 2x + 3y = −7 and 2x − y = 13

Answer: x = 4, y = −5

  1. Subtract equation 2 from equation 1: 4y = −20
  2. y = −5
  3. Substitute into equation 1: 2x − 15 = −7, so x = 4
2.Solve simultaneously: 3x + 4y = −24 and 3x − y = −9

Answer: x = −4, y = −3

  1. Subtract equation 2 from equation 1: 5y = −15
  2. y = −3
  3. Substitute into equation 1: 3x − 12 = −24, so x = −4
3.Solve simultaneously: 2x + 4y = −8 and 2x − 5y = 37

Answer: x = 6, y = −5

  1. Subtract equation 2 from equation 1: 9y = −45
  2. y = −5
  3. Substitute into equation 1: 2x − 20 = −8, so x = 6
4.Solve simultaneously: 4x + y = 18 and 4x − 2y = 12

Answer: x = 4, y = 2

  1. Subtract equation 2 from equation 1: 3y = 6
  2. y = 2
  3. Substitute into equation 1: 4x + 2 = 18, so x = 4
5.Solve simultaneously: 4x + 2y = 12 and 4x − y = 24

Answer: x = 5, y = −4

  1. Subtract equation 2 from equation 1: 3y = −12
  2. y = −4
  3. Substitute into equation 1: 4x − 8 = 12, so x = 5
6.Solve simultaneously: 4x + y = −30 and 4x − 4y = 0

Answer: x = −6, y = −6

  1. Subtract equation 2 from equation 1: 5y = −30
  2. y = −6
  3. Substitute into equation 1: 4x − 6 = −30, so x = −6
7.Solve simultaneously: 2x + 2y = −8 and 2x − 3y = 17

Answer: x = 1, y = −5

  1. Subtract equation 2 from equation 1: 5y = −25
  2. y = −5
  3. Substitute into equation 1: 2x − 10 = −8, so x = 1
8.Solve simultaneously: 3x + 3y = 15 and 3x − 4y = 8

Answer: x = 4, y = 1

  1. Subtract equation 2 from equation 1: 7y = 7
  2. y = 1
  3. Substitute into equation 1: 3x + 3 = 15, 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: