Year 12 Simultaneous Equations Worksheet — Level 1 — Answers
Answer sheet with worked solutions for the Year 12 simultaneous equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Simultaneous EquationsYear 12 Simultaneous Equations Worksheet — Level 1 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: x + y = 3 and x − 3y = 11
Answer: x = 5, y = −2
- Subtract equation 2 from equation 1: 4y = −8
- y = −2
- Substitute into equation 1: x − 2 = 3, so x = 5
2.Solve simultaneously: x + y = 4 and x − 4y = −6
Answer: x = 2, y = 2
- Subtract equation 2 from equation 1: 5y = 10
- y = 2
- Substitute into equation 1: x + 2 = 4, so x = 2
3.Solve simultaneously: x + 3y = −17 and x − 2y = 13
Answer: x = 1, y = −6
- Subtract equation 2 from equation 1: 5y = −30
- y = −6
- Substitute into equation 1: x − 18 = −17, so x = 1
4.Solve simultaneously: x + 3y = −9 and x − 2y = −4
Answer: x = −6, y = −1
- Subtract equation 2 from equation 1: 5y = −5
- y = −1
- Substitute into equation 1: x − 3 = −9, so x = −6
5.Solve simultaneously: x + 3y = 32 and x − 4y = −24
Answer: x = 8, y = 8
- Subtract equation 2 from equation 1: 7y = 56
- y = 8
- Substitute into equation 1: x + 24 = 32, so x = 8
6.Solve simultaneously: x + 3y = 28 and x − 3y = −20
Answer: x = 4, y = 8
- Subtract equation 2 from equation 1: 6y = 48
- y = 8
- Substitute into equation 1: x + 24 = 28, so x = 4
7.Solve simultaneously: x + 4y = 30 and x − 4y = −26
Answer: x = 2, y = 7
- Subtract equation 2 from equation 1: 8y = 56
- y = 7
- Substitute into equation 1: x + 28 = 30, so x = 2
8.Solve simultaneously: x + 2y = −1 and x − 2y = 7
Answer: x = 3, y = −2
- Subtract equation 2 from equation 1: 4y = −8
- y = −2
- Substitute into equation 1: x − 4 = −1, so x = 3
Marking tips
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