y = 2x and x + y = 9
Show answer
(3, 6)
Free printable worksheet
Systems of Equations Worksheet
Twelve systems solved by graphing, substitution, or elimination, including special cases.
Middle School MathGrades 7-84 pagesAnswer key included
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What this worksheet includes
- Twelve systems solved by graphing, substitution, or elimination, including special cases.
- 4-page printable PDF with a complete answer key
- Designed for Grades 7-8 middle school math practice
- Available as an immediate free download with no email required
How to use it
Use this systems of equations 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 7-8 students working on middle school math. 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 Middle School Math worksheets.
Topic guide
How to approach systems of equations
A system's solution satisfies both equations at once. It can be found by graphing, substitution, or elimination, and the most efficient method depends on how the equations are written.
The ordered pair must be checked in both original equations. Parallel lines have no solution, while equivalent equations have infinitely many solutions.
Learning objectives
- Solve systems with multiple methods
- Interpret ordered-pair solutions
- Classify special systems
Skills to review first
- Linear equations
- Graphing lines
- Substitution and combining terms
Worked example
Follow the reasoning step by step
Solve y = x + 1 and 2x + y = 10.
- Substitute x + 1 for y in the second equation.
- Solve 2x + x + 1 = 10.
- Find x = 3, then y = 4.
- Check (3, 4) in both equations.
Solution: (3, 4).
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
x + y = 7 and x − y = 1
Show answer
(4, 3)
y = 3x + 2 and y = 3x − 4
Show answer
No solution
Error check
Common mistakes to watch for
- Checking only one equation
- Writing coordinates in reverse order
- Assuming every system has exactly one solution