Year 11 Simultaneous Equations Worksheet — Level 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 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 2x + 3y = −16 and 4x − 2y = −16
Answer: x = −5, y = −2
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x + 12y = −64 and 8x − 4y = −32
- Subtract: 16y = −32, so y = −2
- Substitute back: x = −5
2.Solve simultaneously: 4x + y = −8 and 2x + 2y = 2
Answer: x = −3, y = 4
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x + 2y = −16 and 8x + 8y = 8
- Subtract: −6y = −24, so y = 4
- Substitute back: x = −3
3.Solve simultaneously: 4x + 3y = −15 and 5x − 2y = −36
Answer: x = −6, y = 3
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x + 15y = −75 and 20x − 8y = −144
- Subtract: 23y = 69, so y = 3
- Substitute back: x = −6
4.Solve simultaneously: 2x − 2y = 10 and 2x − y = 8
Answer: x = 3, y = −2
- Subtract equation 2 from equation 1: −y = 2
- y = −2
- Substitute into equation 1: 2x + 4 = 10, so x = 3
5.Solve simultaneously: 3x + 3y = −12 and 4x + 2y = −10
Answer: x = −1, y = −3
- Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
- 12x + 12y = −48 and 12x + 6y = −30
- Subtract: 6y = −18, so y = −3
- Substitute back: x = −1
6.Solve simultaneously: 2x + 2y = −12 and 4x + y = −9
Answer: x = −1, y = −5
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x + 8y = −48 and 8x + 2y = −18
- Subtract: 6y = −30, so y = −5
- Substitute back: x = −1
7.Solve simultaneously: 3x + 3y = 30 and 4x + 3y = 36
Answer: x = 6, y = 4
- Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
- 12x + 12y = 120 and 12x + 9y = 108
- Subtract: 3y = 12, so y = 4
- Substitute back: x = 6
8.Solve simultaneously: 2x − 2y = 4 and 3x + 4y = −22
Answer: x = −2, y = −4
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x − 6y = 12 and 6x + 8y = −44
- Subtract: −14y = 56, so y = −4
- Substitute back: x = −2
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
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