Year 11 Simultaneous Equations Worksheet — Level 3 — 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 3 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 2x − 3y = 10 and 3x − 2y = 10
Answer: x = 2, y = −2
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x − 9y = 30 and 6x − 4y = 20
- Subtract: −5y = 10, so y = −2
- Substitute back: x = 2
2.Solve simultaneously: 2x − 4y = 36 and 2x − 3y = 30
Answer: x = 6, y = −6
- Subtract equation 2 from equation 1: −y = 6
- y = −6
- Substitute into equation 1: 2x + 24 = 36, so x = 6
3.Solve simultaneously: 2x − 4y = −2 and 3x − 3y = −6
Answer: x = −3, y = −1
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x − 12y = −6 and 6x − 6y = −12
- Subtract: −6y = 6, so y = −1
- Substitute back: x = −3
4.Solve simultaneously: 2x − 3y = 13 and 3x − y = 9
Answer: x = 2, y = −3
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x − 9y = 39 and 6x − 2y = 18
- Subtract: −7y = 21, so y = −3
- Substitute back: x = 2
5.Solve simultaneously: 2x − 2y = −10 and 3x + y = 9
Answer: x = 1, y = 6
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x − 6y = −30 and 6x + 2y = 18
- Subtract: −8y = −48, so y = 6
- Substitute back: x = 1
6.Solve simultaneously: 2x + y = −18 and 2x − 4y = 12
Answer: x = −6, y = −6
- Subtract equation 2 from equation 1: 5y = −30
- y = −6
- Substitute into equation 1: 2x − 6 = −18, so x = −6
7.Solve simultaneously: 3x − 3y = −39 and 2x + 4y = 16
Answer: x = −6, y = 7
- Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
- 6x − 6y = −78 and 6x + 12y = 48
- Subtract: −18y = −126, so y = 7
- Substitute back: x = −6
8.Solve simultaneously: 4x − y = −15 and 3x − y = −11
Answer: x = −4, y = −1
- Multiply equation 1 by 3 and equation 2 by 4 to match the x coefficients
- 12x − 3y = −45 and 12x − 4y = −44
- Subtract: y = −1, so y = −1
- Substitute back: x = −4
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