Year 10 Simultaneous Equations Worksheet — Level 3 — Practice Set 2 — 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 2 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 4x − 2y = 0 and 5x − y = −6
Answer: x = −2, y = −4
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x − 10y = 0 and 20x − 4y = −24
- Subtract: −6y = 24, so y = −4
- Substitute back: x = −2
2.Solve simultaneously: 3x + y = −12 and 4x + 2y = −20
Answer: x = −2, y = −6
- Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
- 12x + 4y = −48 and 12x + 6y = −60
- Subtract: −2y = 12, so y = −6
- Substitute back: x = −2
3.Solve simultaneously: 2x + y = −1 and 5x − y = 8
Answer: x = 1, y = −3
- Multiply equation 1 by 5 and equation 2 by 2 to match the x coefficients
- 10x + 5y = −5 and 10x − 2y = 16
- Subtract: 7y = −21, so y = −3
- Substitute back: x = 1
4.Solve simultaneously: 2x − 2y = −24 and 4x − 5y = −56
Answer: x = −4, y = 8
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x − 8y = −96 and 8x − 10y = −112
- Subtract: 2y = 16, so y = 8
- Substitute back: x = −4
5.Solve simultaneously: 4x + 4y = 0 and 5x + 6y = −3
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 + 24y = −12
- Subtract: −4y = 12, so y = −3
- Substitute back: x = 3
6.Solve simultaneously: 3x + 4y = 25 and 5x − 2y = 33
Answer: x = 7, y = 1
- Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
- 15x + 20y = 125 and 15x − 6y = 99
- Subtract: 26y = 26, so y = 1
- Substitute back: x = 7
7.Solve simultaneously: 4x + 3y = −2 and 2x − 3y = 8
Answer: x = 1, y = −2
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x + 6y = −4 and 8x − 12y = 32
- Subtract: 18y = −36, so y = −2
- Substitute back: x = 1
8.Solve simultaneously: 4x + y = 19 and 2x − 3y = 13
Answer: x = 5, y = −1
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x + 2y = 38 and 8x − 12y = 52
- Subtract: 14y = −14, so y = −1
- Substitute back: x = 5
Marking tips
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