Year 10 Simultaneous Equations Worksheet — Level 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 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 2x − 2y = 28 and 2x − y = 22
Answer: x = 8, y = −6
- Subtract equation 2 from equation 1: −y = 6
- y = −6
- Substitute into equation 1: 2x + 12 = 28, so x = 8
2.Solve simultaneously: 2x + y = 1 and 5x − 3y = −25
Answer: x = −2, y = 5
- Multiply equation 1 by 5 and equation 2 by 2 to match the x coefficients
- 10x + 5y = 5 and 10x − 6y = −50
- Subtract: 11y = 55, so y = 5
- Substitute back: x = −2
3.Solve simultaneously: 2x + y = −2 and 3x + 2y = −6
Answer: x = 2, y = −6
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x + 3y = −6 and 6x + 4y = −12
- Subtract: −y = 6, so y = −6
- Substitute back: x = 2
4.Solve simultaneously: 4x + 2y = 20 and 3x + 4y = 30
Answer: x = 2, y = 6
- Multiply equation 1 by 3 and equation 2 by 4 to match the x coefficients
- 12x + 6y = 60 and 12x + 16y = 120
- Subtract: −10y = −60, so y = 6
- Substitute back: x = 2
5.Solve simultaneously: 2x − 4y = −14 and 3x + 5y = 23
Answer: x = 1, y = 4
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x − 12y = −42 and 6x + 10y = 46
- Subtract: −22y = −88, so y = 4
- Substitute back: x = 1
6.Solve simultaneously: 3x + 4y = 17 and 2x − 3y = −34
Answer: x = −5, y = 8
- Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
- 6x + 8y = 34 and 6x − 9y = −102
- Subtract: 17y = 136, so y = 8
- Substitute back: x = −5
7.Solve simultaneously: 4x − 3y = 7 and 5x − 3y = 14
Answer: x = 7, y = 7
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x − 15y = 35 and 20x − 12y = 56
- Subtract: −3y = −21, so y = 7
- Substitute back: x = 7
8.Solve simultaneously: 2x − y = −13 and 4x − 3y = −31
Answer: x = −4, y = 5
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x − 4y = −52 and 8x − 6y = −62
- Subtract: 2y = 10, so y = 5
- Substitute back: x = −4
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