Systems of Two Equations Worksheets, Grade 8 (8.EE.C.8) – Free PDF + Answer Key

First page of the systems of two equations practice worksheet

Download free

PDFs print on US Letter paper. Free for classroom and home use.

Step-by-step math videos on the Math With Mr DJ YouTube channel →

Key idea

The solution is where the lines meet: both coordinates. Variables cancel and constants disagree → parallel, no solution. Constants agree → same line, infinitely many.

Sample problems

Solve x + y = 7 and x − y = 3.
Solve y = 2x and x + y = 9.
Check whether (2, 5) solves y = 2x + 1 and x + y = 7.
Explain why checking a point in only one equation is not enough.

Common mistakes to watch for

Stopped at x = 4, or gave y without x. Or checked only the first equation — which any point on that line would pass.
Said “he needs to find y as well” without saying why. True and worth partial credit; the reason — that the answer is a location — is what stops it recurring.
Answered x = 0, or gave a point. The variables cancelling is the same signal as in the one-variable lesson, and this is where that recognition pays off.

The answer key explains each one, so you can tell what a wrong answer means.

How to use this set

Teach with the slides (about 15 minutes), or watch the video together.
Practice with the worksheet. Questions climb from fluency to application to reasoning.
Check understanding with the exit ticket, and send the homework home.
Mark with the answer key — each answer shows the steps and the most likely mistake.