Year 10 Simultaneous Equations Worksheet — Level 1 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 10 simultaneous equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Simultaneous EquationsYear 10 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 = −9 and x − 4y = 15
Answer: x = 3, y = −3
- Subtract equation 2 from equation 1: 8y = −24
- y = −3
- Substitute into equation 1: x − 12 = −9, so x = 3
2.Solve simultaneously: x + 2y = 19 and x − 2y = −9
Answer: x = 5, y = 7
- Subtract equation 2 from equation 1: 4y = 28
- y = 7
- Substitute into equation 1: x + 14 = 19, so x = 5
3.Solve simultaneously: x + y = 11 and x − 4y = −9
Answer: x = 7, y = 4
- Subtract equation 2 from equation 1: 5y = 20
- y = 4
- Substitute into equation 1: x + 4 = 11, so x = 7
4.Solve simultaneously: x + y = 3 and x − 3y = 11
Answer: x = 5, y = −2
- Subtract equation 2 from equation 1: 4y = −8
- y = −2
- Substitute into equation 1: x − 2 = 3, so x = 5
5.Solve simultaneously: x + 3y = −22 and x − 2y = 8
Answer: x = −4, y = −6
- Subtract equation 2 from equation 1: 5y = −30
- y = −6
- Substitute into equation 1: x − 18 = −22, so x = −4
6.Solve simultaneously: x + 4y = 1 and x − 3y = −6
Answer: x = −3, y = 1
- Subtract equation 2 from equation 1: 7y = 7
- y = 1
- Substitute into equation 1: x + 4 = 1, so x = −3
7.Solve simultaneously: x + 4y = 5 and x − 4y = −3
Answer: x = 1, y = 1
- Subtract equation 2 from equation 1: 8y = 8
- y = 1
- Substitute into equation 1: x + 4 = 5, so x = 1
8.Solve simultaneously: x + 3y = 2 and x − y = 10
Answer: x = 8, y = −2
- Subtract equation 2 from equation 1: 4y = −8
- y = −2
- Substitute into equation 1: x − 6 = 2, 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.