11th Grade Systems of Equations Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the 11th Grade systems of equations worksheet.
Success TutoringWorksheetsAnswer sheet11th Grade · Mathematics · Simultaneous Equations11th Grade Systems of Equations Worksheet — Level 3 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve the system: 2x + 2y = 10 and 3x + 2y = 17
Answer: x = 7, y = −2
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x + 6y = 30 and 6x + 4y = 34
- Subtract: 2y = −4, so y = −2
- Substitute back: x = 7
2.Solve the system: 3x − 2y = −32 and 2x − 5y = −47
Answer: x = −6, y = 7
- Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
- 6x − 4y = −64 and 6x − 15y = −141
- Subtract: 11y = 77, so y = 7
- Substitute back: x = −6
3.Solve the system: 4x − 3y = −17 and 3x + 2y = −17
Answer: x = −5, y = −1
- Multiply equation 1 by 3 and equation 2 by 4 to match the x coefficients
- 12x − 9y = −51 and 12x + 8y = −68
- Subtract: −17y = 17, so y = −1
- Substitute back: x = −5
4.Solve the system: 2x − 3y = 30 and 5x + 3y = 12
Answer: x = 6, y = −6
- Multiply equation 1 by 5 and equation 2 by 2 to match the x coefficients
- 10x − 15y = 150 and 10x + 6y = 24
- Subtract: −21y = 126, so y = −6
- Substitute back: x = 6
5.Solve the system: 2x − 2y = −4 and 4x + y = −28
Answer: x = −6, y = −4
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x − 8y = −16 and 8x + 2y = −56
- Subtract: −10y = 40, so y = −4
- Substitute back: x = −6
6.Solve the system: 3x + 2y = −11 and 4x + 4y = −12
Answer: x = −5, y = 2
- Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
- 12x + 8y = −44 and 12x + 12y = −36
- Subtract: −4y = −8, so y = 2
- Substitute back: x = −5
7.Solve the system: 3x − 3y = −15 and 5x + y = −1
Answer: x = −1, y = 4
- Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
- 15x − 15y = −75 and 15x + 3y = −3
- Subtract: −18y = −72, so y = 4
- Substitute back: x = −1
8.Solve the system: 3x + 4y = −10 and 3x − 4y = −2
Answer: x = −2, y = −1
- Subtract equation 2 from equation 1: 8y = −8
- y = −1
- Substitute into equation 1: 3x − 4 = −10, so x = −2
Marking tips
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