Year 10 Simultaneous Equations Worksheet — Level 3 — Practice Set 3 — 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 3 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 4x + 2y = 26 and 5x + 4y = 28
Answer: x = 8, y = −3
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x + 10y = 130 and 20x + 16y = 112
- Subtract: −6y = 18, so y = −3
- Substitute back: x = 8
2.Solve simultaneously: 4x + 4y = 0 and 5x + 3y = −6
Answer: x = −3, y = 3
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x + 20y = 0 and 20x + 12y = −24
- Subtract: 8y = 24, so y = 3
- Substitute back: x = −3
3.Solve simultaneously: 3x − y = 19 and 5x − 5y = 45
Answer: x = 5, y = −4
- Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
- 15x − 5y = 95 and 15x − 15y = 135
- Subtract: 10y = −40, so y = −4
- Substitute back: x = 5
4.Solve simultaneously: 4x + 4y = −16 and 4x + y = −7
Answer: x = −1, y = −3
- Subtract equation 2 from equation 1: 3y = −9
- y = −3
- Substitute into equation 1: 4x − 12 = −16, so x = −1
5.Solve simultaneously: 3x − y = −1 and 5x + 4y = −13
Answer: x = −1, y = −2
- Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
- 15x − 5y = −5 and 15x + 12y = −39
- Subtract: −17y = 34, so y = −2
- Substitute back: x = −1
6.Solve simultaneously: 4x − y = −11 and 2x − 2y = −4
Answer: x = −3, y = −1
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x − 2y = −22 and 8x − 8y = −16
- Subtract: 6y = −6, so y = −1
- Substitute back: x = −3
7.Solve simultaneously: 2x − 2y = 0 and 3x + 5y = −32
Answer: x = −4, y = −4
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x − 6y = 0 and 6x + 10y = −64
- Subtract: −16y = 64, so y = −4
- Substitute back: x = −4
8.Solve simultaneously: 3x − 3y = 27 and 5x − y = 25
Answer: x = 4, y = −5
- Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
- 15x − 15y = 135 and 15x − 3y = 75
- Subtract: −12y = 60, 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.
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