y = x + 1 and y = −x + 5
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(2, 3)
Free printable worksheet
Systems by Graphing Worksheet
Nine coordinate-plane systems designed to produce clear integer intersection points.
Algebra 1Grades 7-106 pagesAnswer key included
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What this worksheet includes
- Nine coordinate-plane systems designed to produce clear integer intersection points.
- 6-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 graphing 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 graphing
A solution to a system of linear equations is the ordered pair that lies on both lines. On a graph, that solution appears at the intersection, so accuracy depends on plotting each slope and intercept carefully.
The worksheet uses systems with readable integer intersections and gives each problem its own coordinate plane. Completed answer-key graphs show both lines and label the intersection point.
Learning objectives
- Graph two equations on the same coordinate plane
- Identify the intersection as an ordered-pair solution
- Recognize systems with one, no, or infinitely many solutions
Skills to review first
- Graphing lines
- Slope-intercept form
- Checking ordered pairs
Worked example
Follow the reasoning step by step
Solve y = −x + 3 and y = 2x by graphing.
- Graph y = −x + 3 using (0, 3), (1, 2), and (2, 1).
- Graph y = 2x using (0, 0), (1, 2), and (2, 4).
- Locate the point shared by both lines: (1, 2).
- Check: 2 = −1 + 3 and 2 = 2(1).
Solution: The lines intersect at (1, 2).
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
y = 2x − 4 and y = 2x + 1
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No solution; the lines are parallel.
2x + y = 6 and y = −2x + 6
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Infinitely many solutions; the equations describe the same line.
Error check
Common mistakes to watch for
- Graphing the two equations on separate axes
- Writing the solution as (y, x) instead of (x, y)
- Assuming nearly parallel lines never intersect without checking their slopes