Year 11 Simultaneous Equations Worksheet — Level 1 — 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 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: x + y = 1 and x − 3y = 5
Answer: x = 2, y = −1
- Subtract equation 2 from equation 1: 4y = −4
- y = −1
- Substitute into equation 1: x − 1 = 1, so x = 2
2.Solve simultaneously: x + 4y = 29 and x − 2y = −13
Answer: x = 1, y = 7
- Subtract equation 2 from equation 1: 6y = 42
- y = 7
- Substitute into equation 1: x + 28 = 29, so x = 1
3.Solve simultaneously: x + y = 0 and x − 3y = 24
Answer: x = 6, y = −6
- Subtract equation 2 from equation 1: 4y = −24
- y = −6
- Substitute into equation 1: x − 6 = 0, so x = 6
4.Solve simultaneously: x + 3y = 27 and x − 4y = −29
Answer: x = 3, y = 8
- Subtract equation 2 from equation 1: 7y = 56
- y = 8
- Substitute into equation 1: x + 24 = 27, so x = 3
5.Solve simultaneously: x + y = 2 and x − 4y = −23
Answer: x = −3, y = 5
- Subtract equation 2 from equation 1: 5y = 25
- y = 5
- Substitute into equation 1: x + 5 = 2, so x = −3
6.Solve simultaneously: x + 4y = 31 and x − 4y = −25
Answer: x = 3, y = 7
- Subtract equation 2 from equation 1: 8y = 56
- y = 7
- Substitute into equation 1: x + 28 = 31, so x = 3
7.Solve simultaneously: x + 4y = 2 and x − y = −3
Answer: x = −2, y = 1
- Subtract equation 2 from equation 1: 5y = 5
- y = 1
- Substitute into equation 1: x + 4 = 2, so x = −2
8.Solve simultaneously: x + 4y = 22 and x − 3y = −27
Answer: x = −6, y = 7
- Subtract equation 2 from equation 1: 7y = 49
- y = 7
- Substitute into equation 1: x + 28 = 22, so x = −6
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.
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