Year 11 Simultaneous Equations Worksheet — Level 3 — Practice Set 2 — 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 — Practice Set 2 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 4x + 4y = −8 and 5x + 2y = −16
Answer: x = −4, y = 2
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x + 20y = −40 and 20x + 8y = −64
- Subtract: 12y = 24, so y = 2
- Substitute back: x = −4
2.Solve simultaneously: 3x + y = 16 and 5x + 2y = 29
Answer: x = 3, y = 7
- Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
- 15x + 5y = 80 and 15x + 6y = 87
- Subtract: −y = −7, so y = 7
- Substitute back: x = 3
3.Solve simultaneously: 2x − 4y = −8 and 2x − 3y = −5
Answer: x = 2, y = 3
- Subtract equation 2 from equation 1: −y = −3
- y = 3
- Substitute into equation 1: 2x − 12 = −8, so x = 2
4.Solve simultaneously: 3x + 4y = −2 and 5x − 5y = −15
Answer: x = −2, y = 1
- Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
- 15x + 20y = −10 and 15x − 15y = −45
- Subtract: 35y = 35, so y = 1
- Substitute back: x = −2
5.Solve simultaneously: 2x − 4y = 22 and 3x − y = 3
Answer: x = −1, y = −6
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x − 12y = 66 and 6x − 2y = 6
- Subtract: −10y = 60, so y = −6
- Substitute back: x = −1
6.Solve simultaneously: 3x − 3y = −9 and 4x + 3y = −19
Answer: x = −4, y = −1
- Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
- 12x − 12y = −36 and 12x + 9y = −57
- Subtract: −21y = 21, so y = −1
- Substitute back: x = −4
7.Solve simultaneously: 2x + 3y = 0 and 3x − 3y = −30
Answer: x = −6, y = 4
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x + 9y = 0 and 6x − 6y = −60
- Subtract: 15y = 60, so y = 4
- Substitute back: x = −6
8.Solve simultaneously: 4x + 4y = 28 and 5x + y = 27
Answer: x = 5, y = 2
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x + 20y = 140 and 20x + 4y = 108
- Subtract: 16y = 32, so y = 2
- Substitute back: x = 5
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.