Year 10 Simultaneous Equations Worksheet — Level 1 — Practice Set 3 — 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 3 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: x + 2y = −7 and x − 3y = 18
Answer: x = 3, y = −5
- Subtract equation 2 from equation 1: 5y = −25
- y = −5
- Substitute into equation 1: x − 10 = −7, so x = 3
2.Solve simultaneously: x + 2y = 9 and x − 2y = −7
Answer: x = 1, y = 4
- Subtract equation 2 from equation 1: 4y = 16
- y = 4
- Substitute into equation 1: x + 8 = 9, so x = 1
3.Solve simultaneously: x + 2y = 4 and x − y = 10
Answer: x = 8, y = −2
- Subtract equation 2 from equation 1: 3y = −6
- y = −2
- Substitute into equation 1: x − 4 = 4, so x = 8
4.Solve simultaneously: x + 2y = −9 and x − y = 3
Answer: x = −1, y = −4
- Subtract equation 2 from equation 1: 3y = −12
- y = −4
- Substitute into equation 1: x − 8 = −9, so x = −1
5.Solve simultaneously: x + 3y = −3 and x − 3y = 9
Answer: x = 3, y = −2
- Subtract equation 2 from equation 1: 6y = −12
- y = −2
- Substitute into equation 1: x − 6 = −3, so x = 3
6.Solve simultaneously: x + 3y = 11 and x − 2y = −14
Answer: x = −4, y = 5
- Subtract equation 2 from equation 1: 5y = 25
- y = 5
- Substitute into equation 1: x + 15 = 11, so x = −4
7.Solve simultaneously: x + 2y = 15 and x − 3y = −25
Answer: x = −1, y = 8
- Subtract equation 2 from equation 1: 5y = 40
- y = 8
- Substitute into equation 1: x + 16 = 15, so x = −1
8.Solve simultaneously: x + 4y = 26 and x − 2y = −10
Answer: x = 2, y = 6
- Subtract equation 2 from equation 1: 6y = 36
- y = 6
- Substitute into equation 1: x + 24 = 26, 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.