Year 12 Simultaneous Equations Worksheet — Level 1 — Practice Set 3 — 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 3 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: x + 3y = −8 and x − y = 0
Answer: x = −2, y = −2
- Subtract equation 2 from equation 1: 4y = −8
- y = −2
- Substitute into equation 1: x − 6 = −8, so x = −2
2.Solve simultaneously: x + 4y = 14 and x − 4y = −18
Answer: x = −2, y = 4
- Subtract equation 2 from equation 1: 8y = 32
- y = 4
- Substitute into equation 1: x + 16 = 14, so x = −2
3.Solve simultaneously: x + y = 3 and x − y = −7
Answer: x = −2, y = 5
- Subtract equation 2 from equation 1: 2y = 10
- y = 5
- Substitute into equation 1: x + 5 = 3, so x = −2
4.Solve simultaneously: x + 3y = 14 and x − 4y = −21
Answer: x = −1, y = 5
- Subtract equation 2 from equation 1: 7y = 35
- y = 5
- Substitute into equation 1: x + 15 = 14, so x = −1
5.Solve simultaneously: x + 4y = 39 and x − 2y = −9
Answer: x = 7, y = 8
- Subtract equation 2 from equation 1: 6y = 48
- y = 8
- Substitute into equation 1: x + 32 = 39, so x = 7
6.Solve simultaneously: x + 2y = 2 and x − 3y = 17
Answer: x = 8, y = −3
- Subtract equation 2 from equation 1: 5y = −15
- y = −3
- Substitute into equation 1: x − 6 = 2, so x = 8
7.Solve simultaneously: x + y = −3 and x − 3y = 21
Answer: x = 3, y = −6
- Subtract equation 2 from equation 1: 4y = −24
- y = −6
- Substitute into equation 1: x − 6 = −3, so x = 3
8.Solve simultaneously: x + 3y = −4 and x − 2y = 16
Answer: x = 8, y = −4
- Subtract equation 2 from equation 1: 5y = −20
- y = −4
- Substitute into equation 1: x − 12 = −4, so x = 8
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.