Year 12 Simultaneous Equations Worksheet — Level 1 — Practice Set 4 — 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 4 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: x + 4y = −12 and x − y = 13
Answer: x = 8, y = −5
- Subtract equation 2 from equation 1: 5y = −25
- y = −5
- Substitute into equation 1: x − 20 = −12, so x = 8
2.Solve simultaneously: x + 3y = −15 and x − 2y = 15
Answer: x = 3, y = −6
- Subtract equation 2 from equation 1: 5y = −30
- y = −6
- Substitute into equation 1: x − 18 = −15, so x = 3
3.Solve simultaneously: x + 4y = 11 and x − 3y = −17
Answer: x = −5, y = 4
- Subtract equation 2 from equation 1: 7y = 28
- y = 4
- Substitute into equation 1: x + 16 = 11, so x = −5
4.Solve simultaneously: x + 2y = −1 and x − 2y = −5
Answer: x = −3, y = 1
- Subtract equation 2 from equation 1: 4y = 4
- y = 1
- Substitute into equation 1: x + 2 = −1, so x = −3
5.Solve simultaneously: x + 3y = 1 and x − y = 5
Answer: x = 4, y = −1
- Subtract equation 2 from equation 1: 4y = −4
- y = −1
- Substitute into equation 1: x − 3 = 1, so x = 4
6.Solve simultaneously: x + 2y = 5 and x − 4y = −19
Answer: x = −3, y = 4
- Subtract equation 2 from equation 1: 6y = 24
- y = 4
- Substitute into equation 1: x + 8 = 5, so x = −3
7.Solve simultaneously: x + 2y = −12 and x − 4y = 12
Answer: x = −4, y = −4
- Subtract equation 2 from equation 1: 6y = −24
- y = −4
- Substitute into equation 1: x − 8 = −12, so x = −4
8.Solve simultaneously: x + 4y = 15 and x − 3y = −20
Answer: x = −5, y = 5
- Subtract equation 2 from equation 1: 7y = 35
- y = 5
- Substitute into equation 1: x + 20 = 15, so x = −5
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.