Year 12 Simultaneous Equations Worksheet — Level 1 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 12 simultaneous equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Simultaneous EquationsYear 12 Simultaneous Equations Worksheet — Level 1 — Practice Set 2 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: x + 4y = 29 and x − y = −11
Answer: x = −3, y = 8
- Subtract equation 2 from equation 1: 5y = 40
- y = 8
- Substitute into equation 1: x + 32 = 29, so x = −3
2.Solve simultaneously: x + 3y = 6 and x − 3y = 0
Answer: x = 3, y = 1
- Subtract equation 2 from equation 1: 6y = 6
- y = 1
- Substitute into equation 1: x + 3 = 6, so x = 3
3.Solve simultaneously: x + 4y = 2 and x − y = 7
Answer: x = 6, y = −1
- Subtract equation 2 from equation 1: 5y = −5
- y = −1
- Substitute into equation 1: x − 4 = 2, so x = 6
4.Solve simultaneously: x + y = −4 and x − 4y = 21
Answer: x = 1, y = −5
- Subtract equation 2 from equation 1: 5y = −25
- y = −5
- Substitute into equation 1: x − 5 = −4, so x = 1
5.Solve simultaneously: x + 4y = 7 and x − 4y = −9
Answer: x = −1, y = 2
- Subtract equation 2 from equation 1: 8y = 16
- y = 2
- Substitute into equation 1: x + 8 = 7, so x = −1
6.Solve simultaneously: x + 4y = 9 and x − 4y = −15
Answer: x = −3, y = 3
- Subtract equation 2 from equation 1: 8y = 24
- y = 3
- Substitute into equation 1: x + 12 = 9, so x = −3
7.Solve simultaneously: x + 2y = −13 and x − 3y = 17
Answer: x = −1, y = −6
- Subtract equation 2 from equation 1: 5y = −30
- y = −6
- Substitute into equation 1: x − 12 = −13, so x = −1
8.Solve simultaneously: x + y = 0 and x − 4y = 10
Answer: x = 2, y = −2
- Subtract equation 2 from equation 1: 5y = −10
- y = −2
- Substitute into equation 1: x − 2 = 0, 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.