Solving Systems by Graphing
I can solve a system by graphing both lines and naming the point where they cross.
The problem this sheet solves
A system in two variables needs a value for each, so the solution is a POINT. Students give one coordinate, or give a point that sits on one line only, because checking against both equations is treated as optional. Reading an intersection off a graph that does not cross at a grid corner is the companion problem, and it makes every answer a guess. This sheet requires the answer as an ordered pair and requires it checked in BOTH equations, which is what makes a graphed solution trustworthy rather than approximate. Intersections fall on exact grid points so students read rather than estimate, and the parallel and identical cases both appear.
The key rule
Graph both lines. The solution is the POINT where they cross, so it has two coordinates. Check it in BOTH equations — a point on only one line is not a solution.
The answer is a pair. Check it in both equations.
Watch out
The mistake: Two lines cross at (7, 4), and a student writes the solution is 7.
The fix: The solution is (7, 4). A system in x and y needs a value for each variable, so the 4 is part of the answer, not extra information.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.