Year 10 Simultaneous Equations Worksheet — Level 1 — Practice Set 2 — 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 2 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: x + 4y = 21 and x − 4y = −27
Answer: x = −3, y = 6
- Subtract equation 2 from equation 1: 8y = 48
- y = 6
- Substitute into equation 1: x + 24 = 21, so x = −3
2.Solve simultaneously: x + 4y = −16 and x − 2y = 14
Answer: x = 4, y = −5
- Subtract equation 2 from equation 1: 6y = −30
- y = −5
- Substitute into equation 1: x − 20 = −16, so x = 4
3.Solve simultaneously: x + 4y = 2 and x − 4y = −14
Answer: x = −6, y = 2
- Subtract equation 2 from equation 1: 8y = 16
- y = 2
- Substitute into equation 1: x + 8 = 2, so x = −6
4.Solve simultaneously: x + y = 7 and x − 3y = −9
Answer: x = 3, y = 4
- Subtract equation 2 from equation 1: 4y = 16
- y = 4
- Substitute into equation 1: x + 4 = 7, so x = 3
5.Solve simultaneously: x + 2y = 7 and x − 2y = 3
Answer: x = 5, y = 1
- Subtract equation 2 from equation 1: 4y = 4
- y = 1
- Substitute into equation 1: x + 2 = 7, so x = 5
6.Solve simultaneously: x + 4y = −2 and x − 4y = 6
Answer: x = 2, y = −1
- Subtract equation 2 from equation 1: 8y = −8
- y = −1
- Substitute into equation 1: x − 4 = −2, so x = 2
7.Solve simultaneously: x + 4y = −1 and x − 4y = −9
Answer: x = −5, y = 1
- Subtract equation 2 from equation 1: 8y = 8
- y = 1
- Substitute into equation 1: x + 4 = −1, so x = −5
8.Solve simultaneously: x + 2y = 6 and x − y = 9
Answer: x = 8, y = −1
- Subtract equation 2 from equation 1: 3y = −3
- y = −1
- Substitute into equation 1: x − 2 = 6, 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.