Year 11 Simultaneous Equations Worksheet — Level 2 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 11 simultaneous equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Simultaneous EquationsYear 11 Simultaneous Equations Worksheet — Level 2 — Practice Set 4 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 3x + 3y = 33 and 3x − 2y = 8
Answer: x = 6, y = 5
- Subtract equation 2 from equation 1: 5y = 25
- y = 5
- Substitute into equation 1: 3x + 15 = 33, so x = 6
2.Solve simultaneously: 4x + 4y = 4 and 4x − 3y = −17
Answer: x = −2, y = 3
- Subtract equation 2 from equation 1: 7y = 21
- y = 3
- Substitute into equation 1: 4x + 12 = 4, so x = −2
3.Solve simultaneously: 3x + 3y = 18 and 3x − y = 14
Answer: x = 5, y = 1
- Subtract equation 2 from equation 1: 4y = 4
- y = 1
- Substitute into equation 1: 3x + 3 = 18, so x = 5
4.Solve simultaneously: 2x + 3y = 29 and 2x − y = 9
Answer: x = 7, y = 5
- Subtract equation 2 from equation 1: 4y = 20
- y = 5
- Substitute into equation 1: 2x + 15 = 29, so x = 7
5.Solve simultaneously: 3x + 2y = −6 and 3x − 3y = 24
Answer: x = 2, y = −6
- Subtract equation 2 from equation 1: 5y = −30
- y = −6
- Substitute into equation 1: 3x − 12 = −6, so x = 2
6.Solve simultaneously: 3x + 3y = −3 and 3x − 4y = 25
Answer: x = 3, y = −4
- Subtract equation 2 from equation 1: 7y = −28
- y = −4
- Substitute into equation 1: 3x − 12 = −3, so x = 3
7.Solve simultaneously: 4x + 4y = 16 and 4x − 5y = −29
Answer: x = −1, y = 5
- Subtract equation 2 from equation 1: 9y = 45
- y = 5
- Substitute into equation 1: 4x + 20 = 16, so x = −1
8.Solve simultaneously: 3x + 4y = −36 and 3x − 5y = 18
Answer: x = −4, y = −6
- Subtract equation 2 from equation 1: 9y = −54
- y = −6
- Substitute into equation 1: 3x − 24 = −36, so x = −4
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.