Question

Solve the following system of linear equations by graphing. Graph on your own piece of paper. In your submitted answer, describe what the graph looks like and what this tells you about the solution to the system of linear equations.

y=x+3
𝑦
=
𝑥
+
3

−4x+4y=28

Answer 1

First rewrite the second equation in slope‑intercept form:
-4x + 4y = 28 ⇒ divide by 4 ⇒ -x + y = 7 ⇒ y = x + 7.

The two equations are
y = x + 3
y = x + 7

Both lines have slope 1 (they are parallel) but different y‑intercepts (3 and 7). On your graph you would draw two parallel lines, each rising at 45°, one crossing the y‑axis at (0,3) and the other at (0,7). Because they are parallel, they never meet, so there is no point that satisfies both equations.

Conclusion: the system has no solution (it is inconsistent).