10th Grade Systems of Equations Worksheet — Level 3 — Practice Set 2 — 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 2 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve the system: 3x − y = 2 and 5x − 4y = −6
Answer: x = 2, y = 4
- Multiply equation 1 by 5 and equation 2 by 3 to match the x coefficients
- 15x − 5y = 10 and 15x − 12y = −18
- Subtract: 7y = 28, so y = 4
- Substitute back: x = 2
2.Solve the system: 3x + 2y = −5 and 3x + 3y = −3
Answer: x = −3, y = 2
- Subtract equation 2 from equation 1: −y = −2
- y = 2
- Substitute into equation 1: 3x + 4 = −5, so x = −3
3.Solve the system: 3x − 3y = 9 and 4x − 5y = 18
Answer: x = −3, y = −6
- Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
- 12x − 12y = 36 and 12x − 15y = 54
- Subtract: 3y = −18, so y = −6
- Substitute back: x = −3
4.Solve the system: 4x − 4y = −12 and 2x + 5y = 50
Answer: x = 5, y = 8
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x − 8y = −24 and 8x + 20y = 200
- Subtract: −28y = −224, so y = 8
- Substitute back: x = 5
5.Solve the system: 2x + 2y = 2 and 4x + y = 16
Answer: x = 5, y = −4
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x + 8y = 8 and 8x + 2y = 32
- Subtract: 6y = −24, so y = −4
- Substitute back: x = 5
6.Solve the system: 2x + 3y = 0 and 2x + y = −8
Answer: x = −6, y = 4
- Subtract equation 2 from equation 1: 2y = 8
- y = 4
- Substitute into equation 1: 2x + 12 = 0, so x = −6
7.Solve the system: 2x − y = 12 and 3x − 4y = 28
Answer: x = 4, y = −4
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x − 3y = 36 and 6x − 8y = 56
- Subtract: 5y = −20, so y = −4
- Substitute back: x = 4
8.Solve the system: 2x + 4y = 8 and 4x + 5y = 19
Answer: x = 6, y = −1
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x + 16y = 32 and 8x + 10y = 38
- Subtract: 6y = −6, so y = −1
- Substitute back: x = 6
Marking tips
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