10th Grade Systems of Equations Worksheet — Level 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 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve the system: 2x − 4y = −18 and 4x + 3y = 30
Answer: x = 3, y = 6
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x − 16y = −72 and 8x + 6y = 60
- Subtract: −22y = −132, so y = 6
- Substitute back: x = 3
2.Solve the system: 2x − 2y = −26 and 2x + y = −5
Answer: x = −6, y = 7
- Subtract equation 2 from equation 1: −3y = −21
- y = 7
- Substitute into equation 1: 2x − 14 = −26, so x = −6
3.Solve the system: 2x + 4y = 36 and 4x + 4y = 52
Answer: x = 8, y = 5
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x + 16y = 144 and 8x + 8y = 104
- Subtract: 8y = 40, so y = 5
- Substitute back: x = 8
4.Solve the system: 2x − 4y = 18 and 2x + 2y = 6
Answer: x = 5, y = −2
- Subtract equation 2 from equation 1: −6y = 12
- y = −2
- Substitute into equation 1: 2x + 8 = 18, so x = 5
5.Solve the system: 4x − y = 3 and 2x + 5y = 29
Answer: x = 2, y = 5
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x − 2y = 6 and 8x + 20y = 116
- Subtract: −22y = −110, so y = 5
- Substitute back: x = 2
6.Solve the system: 4x + 4y = 20 and 2x − y = 19
Answer: x = 8, y = −3
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x + 8y = 40 and 8x − 4y = 76
- Subtract: 12y = −36, so y = −3
- Substitute back: x = 8
7.Solve the system: 4x − 3y = 19 and 4x − 5y = 21
Answer: x = 4, y = −1
- Subtract equation 2 from equation 1: 2y = −2
- y = −1
- Substitute into equation 1: 4x + 3 = 19, so x = 4
8.Solve the system: 3x − 4y = −29 and 4x − y = −4
Answer: x = 1, y = 8
- Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
- 12x − 16y = −116 and 12x − 3y = −12
- Subtract: −13y = −104, so y = 8
- Substitute back: x = 1
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