Year 10 Simultaneous Equations Worksheet — Level 3 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 10 simultaneous equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Simultaneous EquationsYear 10 Simultaneous Equations Worksheet — Level 3 — Practice Set 4 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 3x + 2y = 6 and 5x − y = −16
Answer: x = −2, y = 6
- Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
- 15x + 10y = 30 and 15x − 3y = −48
- Subtract: 13y = 78, so y = 6
- Substitute back: x = −2
2.Solve simultaneously: 4x − 2y = 36 and 2x + 0 = 12
Answer: x = 6, y = −6
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x − 4y = 72 and 8x + 0 = 48
- Subtract: −4y = 24, so y = −6
- Substitute back: x = 6
3.Solve simultaneously: 4x + 2y = 2 and 2x + 5y = 21
Answer: x = −2, y = 5
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x + 4y = 4 and 8x + 20y = 84
- Subtract: −16y = −80, so y = 5
- Substitute back: x = −2
4.Solve simultaneously: 3x − y = −5 and 2x − 3y = −8
Answer: x = −1, y = 2
- Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
- 6x − 2y = −10 and 6x − 9y = −24
- Subtract: 7y = 14, so y = 2
- Substitute back: x = −1
5.Solve simultaneously: 3x − y = −20 and 2x + 4y = −4
Answer: x = −6, y = 2
- Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
- 6x − 2y = −40 and 6x + 12y = −12
- Subtract: −14y = −28, so y = 2
- Substitute back: x = −6
6.Solve simultaneously: 2x + 3y = −2 and 2x + 4y = −8
Answer: x = 8, y = −6
- Subtract equation 2 from equation 1: −y = 6
- y = −6
- Substitute into equation 1: 2x − 18 = −2, so x = 8
7.Solve simultaneously: 2x + y = 4 and 2x − 5y = 16
Answer: x = 3, y = −2
- Subtract equation 2 from equation 1: 6y = −12
- y = −2
- Substitute into equation 1: 2x − 2 = 4, so x = 3
8.Solve simultaneously: 4x + 4y = −4 and 5x − y = 25
Answer: x = 4, y = −5
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x + 20y = −20 and 20x − 4y = 100
- Subtract: 24y = −120, so y = −5
- Substitute back: 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.