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 + y = 3 and x − y = 11
Answer: x = 7, y = −4
- Subtract equation 2 from equation 1: 2y = −8
- y = −4
- Substitute into equation 1: x − 4 = 3, so x = 7
2.Solve simultaneously: x + 4y = 18 and x − 3y = −10
Answer: x = 2, y = 4
- Subtract equation 2 from equation 1: 7y = 28
- y = 4
- Substitute into equation 1: x + 16 = 18, so x = 2
3.Solve simultaneously: x + 2y = −11 and x − 3y = 14
Answer: x = −1, y = −5
- Subtract equation 2 from equation 1: 5y = −25
- y = −5
- Substitute into equation 1: x − 10 = −11, so x = −1
4.Solve simultaneously: x + 4y = 26 and x − y = −4
Answer: x = 2, y = 6
- Subtract equation 2 from equation 1: 5y = 30
- y = 6
- Substitute into equation 1: x + 24 = 26, so x = 2
5.Solve simultaneously: x + 2y = 19 and x − 3y = −16
Answer: x = 5, y = 7
- Subtract equation 2 from equation 1: 5y = 35
- y = 7
- Substitute into equation 1: x + 14 = 19, so x = 5
6.Solve simultaneously: x + 3y = 15 and x − 3y = −3
Answer: x = 6, y = 3
- Subtract equation 2 from equation 1: 6y = 18
- y = 3
- Substitute into equation 1: x + 9 = 15, so x = 6
7.Solve simultaneously: x + y = 3 and x − 4y = 28
Answer: x = 8, y = −5
- Subtract equation 2 from equation 1: 5y = −25
- y = −5
- Substitute into equation 1: x − 5 = 3, so x = 8
8.Solve simultaneously: x + y = 1 and x − 4y = −19
Answer: x = −3, y = 4
- Subtract equation 2 from equation 1: 5y = 20
- y = 4
- Substitute into equation 1: x + 4 = 1, so x = −3
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.