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 = 14 and x − y = −11
Answer: x = −6, y = 5
- Subtract equation 2 from equation 1: 5y = 25
- y = 5
- Substitute into equation 1: x + 20 = 14, so x = −6
2.Solve simultaneously: x + 2y = 10 and x − 2y = −6
Answer: x = 2, y = 4
- Subtract equation 2 from equation 1: 4y = 16
- y = 4
- Substitute into equation 1: x + 8 = 10, so x = 2
3.Solve simultaneously: x + 4y = 5 and x − 4y = −11
Answer: x = −3, y = 2
- Subtract equation 2 from equation 1: 8y = 16
- y = 2
- Substitute into equation 1: x + 8 = 5, so x = −3
4.Solve simultaneously: x + 2y = 13 and x − 3y = −17
Answer: x = 1, y = 6
- Subtract equation 2 from equation 1: 5y = 30
- y = 6
- Substitute into equation 1: x + 12 = 13, so x = 1
5.Solve simultaneously: x + 2y = 19 and x − y = −2
Answer: x = 5, y = 7
- Subtract equation 2 from equation 1: 3y = 21
- y = 7
- Substitute into equation 1: x + 14 = 19, so x = 5
6.Solve simultaneously: x + y = −9 and x − y = −3
Answer: x = −6, y = −3
- Subtract equation 2 from equation 1: 2y = −6
- y = −3
- Substitute into equation 1: x − 3 = −9, so x = −6
7.Solve simultaneously: x + 3y = 10 and x − y = −6
Answer: x = −2, y = 4
- Subtract equation 2 from equation 1: 4y = 16
- y = 4
- Substitute into equation 1: x + 12 = 10, so x = −2
8.Solve simultaneously: x + 4y = 30 and x − 3y = −26
Answer: x = −2, y = 8
- Subtract equation 2 from equation 1: 7y = 56
- y = 8
- Substitute into equation 1: x + 32 = 30, 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.