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: 2x + y = 22 and 4x − 5y = 2
Answer: x = 8, y = 6
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x + 4y = 88 and 8x − 10y = 4
- Subtract: 14y = 84, so y = 6
- Substitute back: x = 8
2.Solve simultaneously: 2x − 2y = −2 and 5x − 3y = −9
Answer: x = −3, y = −2
- Multiply equation 1 by 5 and equation 2 by 2 to match the x coefficients
- 10x − 10y = −10 and 10x − 6y = −18
- Subtract: −4y = 8, so y = −2
- Substitute back: x = −3
3.Solve simultaneously: 3x − 4y = −30 and 4x − y = −27
Answer: x = −6, y = 3
- Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
- 12x − 16y = −120 and 12x − 3y = −81
- Subtract: −13y = −39, so y = 3
- Substitute back: x = −6
4.Solve simultaneously: 3x − y = 13 and 2x + 3y = 16
Answer: x = 5, y = 2
- Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
- 6x − 2y = 26 and 6x + 9y = 48
- Subtract: −11y = −22, so y = 2
- Substitute back: x = 5
5.Solve simultaneously: 3x − 3y = −9 and 5x − 3y = −1
Answer: x = 4, y = 7
- Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
- 15x − 15y = −45 and 15x − 9y = −3
- Subtract: −6y = −42, so y = 7
- Substitute back: x = 4
6.Solve simultaneously: 2x + 3y = 5 and 4x − 3y = −35
Answer: x = −5, y = 5
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x + 12y = 20 and 8x − 6y = −70
- Subtract: 18y = 90, so y = 5
- Substitute back: x = −5
7.Solve simultaneously: 3x − 4y = 36 and 5x − 3y = 38
Answer: x = 4, y = −6
- Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
- 15x − 20y = 180 and 15x − 9y = 114
- Subtract: −11y = 66, so y = −6
- Substitute back: x = 4
8.Solve simultaneously: 2x − y = −10 and 5x − y = −22
Answer: x = −4, y = 2
- Multiply equation 1 by 5 and equation 2 by 2 to match the x coefficients
- 10x − 5y = −50 and 10x − 2y = −44
- Subtract: −3y = −6, so y = 2
- Substitute back: x = −4
Marking tips
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