10th Grade Systems of Equations Worksheet — Level 3 — Practice Set 3 — Answers
Answer sheet with worked solutions for the 10th Grade systems of equations worksheet.
Success TutoringWorksheetsAnswer sheet10th Grade · Mathematics · Simultaneous Equations10th Grade Systems of Equations Worksheet — Level 3 — Practice Set 3 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve the system: 2x + y = −4 and 4x − 2y = 16
Answer: x = 1, y = −6
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x + 4y = −16 and 8x − 4y = 32
- Subtract: 8y = −48, so y = −6
- Substitute back: x = 1
2.Solve the system: 2x + 2y = 0 and 3x + y = −8
Answer: x = −4, y = 4
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x + 6y = 0 and 6x + 2y = −16
- Subtract: 4y = 16, so y = 4
- Substitute back: x = −4
3.Solve the system: 4x + y = 35 and 2x − 2y = 0
Answer: x = 7, y = 7
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x + 2y = 70 and 8x − 8y = 0
- Subtract: 10y = 70, so y = 7
- Substitute back: x = 7
4.Solve the system: 2x − 4y = 6 and 2x + 4y = −26
Answer: x = −5, y = −4
- Subtract equation 2 from equation 1: −8y = 32
- y = −4
- Substitute into equation 1: 2x + 16 = 6, so x = −5
5.Solve the system: 3x − 4y = 22 and 5x − 3y = 33
Answer: x = 6, y = −1
- Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
- 15x − 20y = 110 and 15x − 9y = 99
- Subtract: −11y = 11, so y = −1
- Substitute back: x = 6
6.Solve the system: 4x − 4y = 16 and 4x − 5y = 22
Answer: x = −2, y = −6
- Subtract equation 2 from equation 1: y = −6
- y = −6
- Substitute into equation 1: 4x + 24 = 16, so x = −2
7.Solve the system: 4x + y = −22 and 4x + 2y = −28
Answer: x = −4, y = −6
- Subtract equation 2 from equation 1: −y = 6
- y = −6
- Substitute into equation 1: 4x − 6 = −22, so x = −4
8.Solve the system: 4x − 4y = 48 and 5x − 2y = 42
Answer: x = 6, y = −6
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x − 20y = 240 and 20x − 8y = 168
- Subtract: −12y = 72, so y = −6
- Substitute back: x = 6
Marking tips
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