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: 2x − 4y = 8 and 2x + 3y = 15
Answer: x = 6, y = 1
- Subtract equation 2 from equation 1: −7y = −7
- y = 1
- Substitute into equation 1: 2x − 4 = 8, so x = 6
2.Solve simultaneously: 4x + 2y = 38 and 4x + y = 35
Answer: x = 8, y = 3
- Subtract equation 2 from equation 1: y = 3
- y = 3
- Substitute into equation 1: 4x + 6 = 38, so x = 8
3.Solve simultaneously: 2x + 4y = 28 and 3x + 4y = 36
Answer: x = 8, y = 3
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x + 12y = 84 and 6x + 8y = 72
- Subtract: 4y = 12, so y = 3
- Substitute back: x = 8
4.Solve simultaneously: 2x + 4y = 4 and 3x − y = −8
Answer: x = −2, y = 2
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x + 12y = 12 and 6x − 2y = −16
- Subtract: 14y = 28, so y = 2
- Substitute back: x = −2
5.Solve simultaneously: 3x + y = 16 and 2x + 2y = 8
Answer: x = 6, y = −2
- Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
- 6x + 2y = 32 and 6x + 6y = 24
- Subtract: −4y = 8, so y = −2
- Substitute back: x = 6
6.Solve simultaneously: 4x + 4y = 8 and 3x + 5y = 12
Answer: x = −1, y = 3
- Multiply equation 1 by 3 and equation 2 by 4 to match the x coefficients
- 12x + 12y = 24 and 12x + 20y = 48
- Subtract: −8y = −24, so y = 3
- Substitute back: x = −1
7.Solve simultaneously: 3x − 4y = −23 and 5x − 5y = −35
Answer: x = −5, y = 2
- Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
- 15x − 20y = −115 and 15x − 15y = −105
- Subtract: −5y = −10, so y = 2
- Substitute back: x = −5
8.Solve simultaneously: 2x − 2y = 12 and 2x + 4y = 24
Answer: x = 8, y = 2
- Subtract equation 2 from equation 1: −6y = −12
- y = 2
- Substitute into equation 1: 2x − 4 = 12, so x = 8
Marking tips
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