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 + y = 6 and x − y = 4
Answer: x = 5, y = 1
- Subtract equation 2 from equation 1: 2y = 2
- y = 1
- Substitute into equation 1: x + 1 = 6, so x = 5
2.Solve simultaneously: x + 4y = −1 and x − 2y = 5
Answer: x = 3, y = −1
- Subtract equation 2 from equation 1: 6y = −6
- y = −1
- Substitute into equation 1: x − 4 = −1, so x = 3
3.Solve simultaneously: x + 4y = −14 and x − 3y = 7
Answer: x = −2, y = −3
- Subtract equation 2 from equation 1: 7y = −21
- y = −3
- Substitute into equation 1: x − 12 = −14, so x = −2
4.Solve simultaneously: x + 4y = 20 and x − 4y = −4
Answer: x = 8, y = 3
- Subtract equation 2 from equation 1: 8y = 24
- y = 3
- Substitute into equation 1: x + 12 = 20, so x = 8
5.Solve simultaneously: x + 3y = 15 and x − 4y = −13
Answer: x = 3, y = 4
- Subtract equation 2 from equation 1: 7y = 28
- y = 4
- Substitute into equation 1: x + 12 = 15, so x = 3
6.Solve simultaneously: x + 2y = 13 and x − y = −2
Answer: x = 3, y = 5
- Subtract equation 2 from equation 1: 3y = 15
- y = 5
- Substitute into equation 1: x + 10 = 13, so x = 3
7.Solve simultaneously: x + 2y = 16 and x − 4y = −14
Answer: x = 6, y = 5
- Subtract equation 2 from equation 1: 6y = 30
- y = 5
- Substitute into equation 1: x + 10 = 16, so x = 6
8.Solve simultaneously: x + 2y = 1 and x − 3y = −14
Answer: x = −5, y = 3
- Subtract equation 2 from equation 1: 5y = 15
- y = 3
- Substitute into equation 1: x + 6 = 1, 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.