Year 11 Simultaneous Equations Worksheet — Level 1 — Practice Set 3 — 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 3 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: x + 2y = 3 and x − 2y = 11
Answer: x = 7, y = −2
- Subtract equation 2 from equation 1: 4y = −8
- y = −2
- Substitute into equation 1: x − 4 = 3, so x = 7
2.Solve simultaneously: x + 4y = −8 and x − y = 7
Answer: x = 4, y = −3
- Subtract equation 2 from equation 1: 5y = −15
- y = −3
- Substitute into equation 1: x − 12 = −8, so x = 4
3.Solve simultaneously: x + 3y = 21 and x − 2y = −4
Answer: x = 6, y = 5
- Subtract equation 2 from equation 1: 5y = 25
- y = 5
- Substitute into equation 1: x + 15 = 21, so x = 6
4.Solve simultaneously: x + 4y = 23 and x − y = 3
Answer: x = 7, y = 4
- Subtract equation 2 from equation 1: 5y = 20
- y = 4
- Substitute into equation 1: x + 16 = 23, so x = 7
5.Solve simultaneously: x + 2y = 15 and x − 2y = −13
Answer: x = 1, y = 7
- Subtract equation 2 from equation 1: 4y = 28
- y = 7
- Substitute into equation 1: x + 14 = 15, so x = 1
6.Solve simultaneously: x + y = 7 and x − 3y = −17
Answer: x = 1, y = 6
- Subtract equation 2 from equation 1: 4y = 24
- y = 6
- Substitute into equation 1: x + 6 = 7, so x = 1
7.Solve simultaneously: x + 3y = 13 and x − 4y = −22
Answer: x = −2, y = 5
- Subtract equation 2 from equation 1: 7y = 35
- y = 5
- Substitute into equation 1: x + 15 = 13, so x = −2
8.Solve simultaneously: x + 4y = −8 and x − y = 12
Answer: x = 8, y = −4
- Subtract equation 2 from equation 1: 5y = −20
- y = −4
- Substitute into equation 1: x − 16 = −8, 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.