x + 2y = 8 and 3x − 2y = 8
Show answer
(4, 2)
Free printable worksheet
Systems by Elimination Worksheet
Fourteen advanced systems requiring rearrangement, scaling, simplification, and elimination.
Algebra 1Grades 7-104 pagesAnswer key included
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What this worksheet includes
- Fourteen advanced systems requiring rearrangement, scaling, simplification, and elimination.
- 4-page printable PDF with a complete answer key
- Designed for Grades 7-10 algebra 1 practice
- Available as an immediate free download with no email required
How to use it
Use this systems by elimination worksheet for guided practice, independent review, homework, tutoring sessions, or a quick skills check. The spacious layout is designed to leave room for students to show their work rather than guess from crowded answer choices.
After students finish, compare their reasoning with the included answer key. When an answer is incorrect, have the student locate the first step where their work changed direction before trying the problem again.
Who this practice is for
This resource is designed for grades 7-10 students working on algebra 1. Teachers, tutors, homeschool families, and parents can preview the first page before deciding whether the level and spacing fit the student.
Looking for a broader sequence? Browse all Algebra I worksheets.
Topic guide
How to approach systems by elimination
Elimination combines two equations so one variable cancels. Some systems are ready to add immediately; others require rearranging terms or multiplying one or both equations by constants first.
The later problems intentionally avoid matching coefficients. Students must choose an efficient least common multiple, scale every term in an equation, and then check the ordered pair in both original equations.
Learning objectives
- Choose whether to add or subtract equations
- Scale one or both equations to create opposite coefficients
- Substitute back and verify the ordered-pair solution
Skills to review first
- Combining like terms
- Multiplying an entire equation by a constant
- Solving one-variable equations
Worked example
Follow the reasoning step by step
Solve 2x + 3y = 12 and 5x − 3y = 9.
- Add the equations so +3y and −3y cancel.
- Simplify: 7x = 21, so x = 3.
- Substitute x = 3 into 2x + 3y = 12.
- Solve 6 + 3y = 12 to get y = 2.
Solution: (3, 2); it satisfies both original equations.
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
2x + y = 7 and 3x + 2y = 12
Show answer
Multiply the first equation by −2; solution (2, 3).
2x + 3y = 7 and 5x − 2y = 8
Show answer
Scale both equations; solution (2, 1).
Error check
Common mistakes to watch for
- Multiplying only the variable terms and not the constant
- Adding coefficients that should cancel
- Stopping after finding one coordinate