Year 11 Simultaneous Equations Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 11 simultaneous equations worksheet.
Year 11 · Mathematics · Simultaneous Equations
Year 11 Simultaneous Equations Worksheet — Level 3 — Answers
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Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 4x + y = −16 and 5x + 2y = −14
Answer: x = −6, y = 8
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x + 5y = −80 and 20x + 8y = −56
- Subtract: −3y = −24, so y = 8
- Substitute back: x = −6
2.Solve simultaneously: 2x + 4y = 12 and 3x + 3y = 3
Answer: x = −4, y = 5
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x + 12y = 36 and 6x + 6y = 6
- Subtract: 6y = 30, so y = 5
- Substitute back: x = −4
3.Solve simultaneously: 4x − 4y = −16 and 5x + 5y = −40
Answer: x = −6, y = −2
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x − 20y = −80 and 20x + 20y = −160
- Subtract: −40y = 80, so y = −2
- Substitute back: x = −6
4.Solve simultaneously: 2x + 4y = −10 and 3x − 2y = −7
Answer: x = −3, y = −1
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x + 12y = −30 and 6x − 4y = −14
- Subtract: 16y = −16, so y = −1
- Substitute back: x = −3
5.Solve simultaneously: 3x + 4y = 44 and 5x − y = 12
Answer: x = 4, y = 8
- Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
- 15x + 20y = 220 and 15x − 3y = 36
- Subtract: 23y = 184, so y = 8
- Substitute back: x = 4
6.Solve simultaneously: 3x + 3y = −3 and 2x − 5y = 12
Answer: x = 1, y = −2
- Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
- 6x + 6y = −6 and 6x − 15y = 36
- Subtract: 21y = −42, so y = −2
- Substitute back: x = 1
7.Solve simultaneously: 4x + 2y = 30 and 3x + 4y = 25
Answer: x = 7, y = 1
- Multiply equation 1 by 3 and equation 2 by 4 to match the x coefficients
- 12x + 6y = 90 and 12x + 16y = 100
- Subtract: −10y = −10, so y = 1
- Substitute back: x = 7
8.Solve simultaneously: 4x + 2y = 38 and 4x + 3y = 43
Answer: x = 7, y = 5
- Subtract equation 2 from equation 1: −y = −5
- y = 5
- Substitute into equation 1: 4x + 10 = 38, so x = 7
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