Year 11 Simultaneous Equations Worksheet — Level 3 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 11 simultaneous equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Simultaneous EquationsYear 11 Simultaneous Equations Worksheet — Level 3 — Practice Set 4 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 3x + 2y = −26 and 2x + 4y = −28
Answer: x = −6, y = −4
- Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
- 6x + 4y = −52 and 6x + 12y = −84
- Subtract: −8y = 32, so y = −4
- Substitute back: x = −6
2.Solve simultaneously: 4x − 3y = −35 and 5x − 2y = −35
Answer: x = −5, y = 5
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x − 15y = −175 and 20x − 8y = −140
- Subtract: −7y = −35, so y = 5
- Substitute back: x = −5
3.Solve simultaneously: 4x − 4y = 16 and 4x + 4y = −24
Answer: x = −1, y = −5
- Subtract equation 2 from equation 1: −8y = 40
- y = −5
- Substitute into equation 1: 4x + 20 = 16, so x = −1
4.Solve simultaneously: 4x − 2y = −4 and 2x + 5y = −38
Answer: x = −4, y = −6
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x − 4y = −8 and 8x + 20y = −152
- Subtract: −24y = 144, so y = −6
- Substitute back: x = −4
5.Solve simultaneously: 3x + y = 1 and 5x + 3y = −1
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 + 9y = −3
- Subtract: −4y = 8, so y = −2
- Substitute back: x = 1
6.Solve simultaneously: 2x + 3y = 12 and 4x − 4y = −56
Answer: x = −6, y = 8
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x + 12y = 48 and 8x − 8y = −112
- Subtract: 20y = 160, so y = 8
- Substitute back: x = −6
7.Solve simultaneously: 4x + 3y = −27 and 4x + 4y = −28
Answer: x = −6, y = −1
- Subtract equation 2 from equation 1: −y = 1
- y = −1
- Substitute into equation 1: 4x − 3 = −27, so x = −6
8.Solve simultaneously: 2x + 3y = 13 and 2x + 5y = 11
Answer: x = 8, y = −1
- Subtract equation 2 from equation 1: −2y = 2
- y = −1
- Substitute into equation 1: 2x − 3 = 13, so x = 8
Marking tips
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