Year 11 Simultaneous Equations Worksheet — Level 1 — Practice Set 4 — 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 1 — Practice Set 4 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: x + 3y = 28 and x − y = 0
Answer: x = 7, y = 7
- Subtract equation 2 from equation 1: 4y = 28
- y = 7
- Substitute into equation 1: x + 21 = 28, so x = 7
2.Solve simultaneously: x + 4y = 14 and x − y = −6
Answer: x = −2, y = 4
- Subtract equation 2 from equation 1: 5y = 20
- y = 4
- Substitute into equation 1: x + 16 = 14, so x = −2
3.Solve simultaneously: x + 4y = −23 and x − y = 2
Answer: x = −3, y = −5
- Subtract equation 2 from equation 1: 5y = −25
- y = −5
- Substitute into equation 1: x − 20 = −23, so x = −3
4.Solve simultaneously: x + y = 1 and x − y = −5
Answer: x = −2, y = 3
- Subtract equation 2 from equation 1: 2y = 6
- y = 3
- Substitute into equation 1: x + 3 = 1, so x = −2
5.Solve simultaneously: x + 4y = 31 and x − 4y = −17
Answer: x = 7, y = 6
- Subtract equation 2 from equation 1: 8y = 48
- y = 6
- Substitute into equation 1: x + 24 = 31, so x = 7
6.Solve simultaneously: x + 4y = −5 and x − y = 0
Answer: x = −1, y = −1
- Subtract equation 2 from equation 1: 5y = −5
- y = −1
- Substitute into equation 1: x − 4 = −5, so x = −1
7.Solve simultaneously: x + y = 7 and x − 2y = 1
Answer: x = 5, y = 2
- Subtract equation 2 from equation 1: 3y = 6
- y = 2
- Substitute into equation 1: x + 2 = 7, so x = 5
8.Solve simultaneously: x + 3y = 4 and x − 2y = −6
Answer: x = −2, y = 2
- Subtract equation 2 from equation 1: 5y = 10
- y = 2
- Substitute into equation 1: x + 6 = 4, 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.