Year 11 Simultaneous Equations Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 11 simultaneous equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Simultaneous EquationsYear 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 + y = 0 and 2x − 2y = −6
Answer: x = −1, y = 2
- Subtract equation 2 from equation 1: 3y = 6
- y = 2
- Substitute into equation 1: 2x + 2 = 0, so x = −1
2.Solve simultaneously: 2x + y = 17 and 2x − 3y = 5
Answer: x = 7, y = 3
- Subtract equation 2 from equation 1: 4y = 12
- y = 3
- Substitute into equation 1: 2x + 3 = 17, so x = 7
3.Solve simultaneously: 4x + 4y = −12 and 4x − y = 13
Answer: x = 2, y = −5
- Subtract equation 2 from equation 1: 5y = −25
- y = −5
- Substitute into equation 1: 4x − 20 = −12, so x = 2
4.Solve simultaneously: 2x + y = 9 and 2x − 2y = 18
Answer: x = 6, y = −3
- Subtract equation 2 from equation 1: 3y = −9
- y = −3
- Substitute into equation 1: 2x − 3 = 9, so x = 6
5.Solve simultaneously: 3x + 2y = 22 and 3x − y = 7
Answer: x = 4, y = 5
- Subtract equation 2 from equation 1: 3y = 15
- y = 5
- Substitute into equation 1: 3x + 10 = 22, so x = 4
6.Solve simultaneously: 4x + 4y = 16 and 4x − 2y = 10
Answer: x = 3, y = 1
- Subtract equation 2 from equation 1: 6y = 6
- y = 1
- Substitute into equation 1: 4x + 4 = 16, so x = 3
7.Solve simultaneously: 3x + y = −22 and 3x − 4y = −2
Answer: x = −6, y = −4
- Subtract equation 2 from equation 1: 5y = −20
- y = −4
- Substitute into equation 1: 3x − 4 = −22, so x = −6
8.Solve simultaneously: 3x + y = −2 and 3x − 2y = −14
Answer: x = −2, y = 4
- Subtract equation 2 from equation 1: 3y = 12
- y = 4
- Substitute into equation 1: 3x + 4 = −2, so x = −2
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.