10th Grade Systems of Equations Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve the system: 3x + 4y = −17 and 2x − y = −4
Answer: x = −3, y = −2
- Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
- 6x + 8y = −34 and 6x − 3y = −12
- Subtract: 11y = −22, so y = −2
- Substitute back: x = −3
2.Solve the system: 2x + 3y = −6 and 5x + 3y = 3
Answer: x = 3, y = −4
- Multiply equation 1 by 5 and equation 2 by 2 to match the x coefficients
- 10x + 15y = −30 and 10x + 6y = 6
- Subtract: 9y = −36, so y = −4
- Substitute back: x = 3
3.Solve the system: 4x + 2y = 18 and 5x + y = 21
Answer: x = 4, y = 1
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x + 10y = 90 and 20x + 4y = 84
- Subtract: 6y = 6, so y = 1
- Substitute back: x = 4
4.Solve the system: 2x + 4y = 10 and 3x + 5y = 13
Answer: x = 1, y = 2
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x + 12y = 30 and 6x + 10y = 26
- Subtract: 2y = 4, so y = 2
- Substitute back: x = 1
5.Solve the system: 2x + y = 7 and 3x − 3y = −12
Answer: x = 1, y = 5
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x + 3y = 21 and 6x − 6y = −24
- Subtract: 9y = 45, so y = 5
- Substitute back: x = 1
6.Solve the system: 3x + y = 9 and 2x + 5y = 32
Answer: x = 1, y = 6
- Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
- 6x + 2y = 18 and 6x + 15y = 96
- Subtract: −13y = −78, so y = 6
- Substitute back: x = 1
7.Solve the system: 3x + 2y = 20 and 4x + 3y = 29
Answer: x = 2, y = 7
- Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
- 12x + 8y = 80 and 12x + 9y = 87
- Subtract: −y = −7, so y = 7
- Substitute back: x = 2
8.Solve the system: 4x + 4y = 0 and 5x − y = 30
Answer: x = 5, y = −5
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x + 20y = 0 and 20x − 4y = 120
- Subtract: 24y = −120, so y = −5
- Substitute back: x = 5
Marking tips
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