Year 11 Simultaneous Equations Worksheet — Level 3 — Practice Set 3 — 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 3 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 4x + 3y = −11 and 3x − 4y = 23
Answer: x = 1, y = −5
- Multiply equation 1 by 3 and equation 2 by 4 to match the x coefficients
- 12x + 9y = −33 and 12x − 16y = 92
- Subtract: 25y = −125, so y = −5
- Substitute back: x = 1
2.Solve simultaneously: 2x − y = −1 and 2x − 4y = 2
Answer: x = −1, y = −1
- Subtract equation 2 from equation 1: 3y = −3
- y = −1
- Substitute into equation 1: 2x + 1 = −1, so x = −1
3.Solve simultaneously: 2x − y = −15 and 4x − 5y = −45
Answer: x = −5, y = 5
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x − 4y = −60 and 8x − 10y = −90
- Subtract: 6y = 30, so y = 5
- Substitute back: x = −5
4.Solve simultaneously: 4x − 4y = 36 and 3x − 2y = 26
Answer: x = 8, y = −1
- Multiply equation 1 by 3 and equation 2 by 4 to match the x coefficients
- 12x − 12y = 108 and 12x − 8y = 104
- Subtract: −4y = 4, so y = −1
- Substitute back: x = 8
5.Solve simultaneously: 3x + 3y = 36 and 3x − 2y = 11
Answer: x = 7, y = 5
- Subtract equation 2 from equation 1: 5y = 25
- y = 5
- Substitute into equation 1: 3x + 15 = 36, so x = 7
6.Solve simultaneously: 3x + 2y = 22 and 3x + 3y = 24
Answer: x = 6, y = 2
- Subtract equation 2 from equation 1: −y = −2
- y = 2
- Substitute into equation 1: 3x + 4 = 22, so x = 6
7.Solve simultaneously: 2x + 3y = −5 and 3x + 4y = −7
Answer: x = −1, y = −1
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x + 9y = −15 and 6x + 8y = −14
- Subtract: y = −1, so y = −1
- Substitute back: x = −1
8.Solve simultaneously: 2x + 2y = −12 and 3x + 2y = −14
Answer: x = −2, y = −4
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x + 6y = −36 and 6x + 4y = −28
- Subtract: 2y = −8, so y = −4
- Substitute back: x = −2
Marking tips
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