Year 9 Simultaneous Equations Worksheet — Level 3 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 9 simultaneous equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Simultaneous EquationsYear 9 Simultaneous Equations Worksheet — Level 3 — Practice Set 4 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 2x + 3y = −1 and 2x + 4y = −2
Answer: x = 1, y = −1
- Subtract equation 2 from equation 1: −y = 1
- y = −1
- Substitute into equation 1: 2x − 3 = −1, so x = 1
2.Solve simultaneously: 3x − 3y = 12 and 5x + 5y = −40
Answer: x = −2, y = −6
- Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
- 15x − 15y = 60 and 15x + 15y = −120
- Subtract: −30y = 180, so y = −6
- Substitute back: x = −2
3.Solve simultaneously: 4x − 2y = −14 and 2x + 3y = −19
Answer: x = −5, y = −3
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x − 4y = −28 and 8x + 12y = −76
- Subtract: −16y = 48, so y = −3
- Substitute back: x = −5
4.Solve simultaneously: 2x + 4y = 12 and 4x − 3y = 35
Answer: x = 8, y = −1
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x + 16y = 48 and 8x − 6y = 70
- Subtract: 22y = −22, so y = −1
- Substitute back: x = 8
5.Solve simultaneously: 2x + y = 11 and 5x + 3y = 27
Answer: x = 6, y = −1
- Multiply equation 1 by 5 and equation 2 by 2 to match the x coefficients
- 10x + 5y = 55 and 10x + 6y = 54
- Subtract: −y = 1, so y = −1
- Substitute back: x = 6
6.Solve simultaneously: 3x − 4y = −10 and 3x + y = −20
Answer: x = −6, y = −2
- Subtract equation 2 from equation 1: −5y = 10
- y = −2
- Substitute into equation 1: 3x + 8 = −10, so x = −6
7.Solve simultaneously: 4x − 4y = 4 and 5x − y = 9
Answer: x = 2, y = 1
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x − 20y = 20 and 20x − 4y = 36
- Subtract: −16y = −16, so y = 1
- Substitute back: x = 2
8.Solve simultaneously: 3x − 2y = 4 and 5x + 4y = 14
Answer: x = 2, y = 1
- Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
- 15x − 10y = 20 and 15x + 12y = 42
- Subtract: −22y = −22, so y = 1
- Substitute back: x = 2
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.