11th Grade Systems of Equations Worksheet — Level 3 — Practice Set 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 — Practice Set 3 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve the system: 2x − 3y = 10 and 2x + y = 2
Answer: x = 2, y = −2
- Subtract equation 2 from equation 1: −4y = 8
- y = −2
- Substitute into equation 1: 2x + 6 = 10, so x = 2
2.Solve the system: 3x + 3y = −15 and 5x + 4y = −21
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 + 12y = −63
- Subtract: 3y = −12, so y = −4
- Substitute back: x = −1
3.Solve the system: 4x − 4y = −24 and 2x + 4y = −6
Answer: x = −5, y = 1
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x − 8y = −48 and 8x + 16y = −24
- Subtract: −24y = −24, so y = 1
- Substitute back: x = −5
4.Solve the system: 3x + y = 19 and 4x + 5y = 7
Answer: x = 8, y = −5
- Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
- 12x + 4y = 76 and 12x + 15y = 21
- Subtract: −11y = 55, so y = −5
- Substitute back: x = 8
5.Solve the system: 3x + 2y = −9 and 2x + y = −5
Answer: x = −1, y = −3
- Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
- 6x + 4y = −18 and 6x + 3y = −15
- Subtract: y = −3, so y = −3
- Substitute back: x = −1
6.Solve the system: 3x + y = 11 and 3x + 4y = 17
Answer: x = 3, y = 2
- Subtract equation 2 from equation 1: −3y = −6
- y = 2
- Substitute into equation 1: 3x + 2 = 11, so x = 3
7.Solve the system: 4x − 2y = −26 and 3x + 5y = −13
Answer: x = −6, y = 1
- Multiply equation 1 by 3 and equation 2 by 4 to match the x coefficients
- 12x − 6y = −78 and 12x + 20y = −52
- Subtract: −26y = −26, so y = 1
- Substitute back: x = −6
8.Solve the system: 4x + y = 6 and 2x − y = 6
Answer: x = 2, y = −2
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x + 2y = 12 and 8x − 4y = 24
- Subtract: 6y = −12, so y = −2
- Substitute back: x = 2
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
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