Question

Which of the graphs with no solution correctly shows the system of equations y=2x+4
𝑦
=
2
𝑥
+
4
and −2x+y=8
−
2
𝑥
+
𝑦
=
8
?

Answer 1

Solve each for y: the first is y = 2x + 4. The second gives y = 2x + 8.

Both lines have slope 2 but different y‑intercepts (4 and 8), so they are parallel and never meet (no solution).

The correct graph shows two parallel lines with slope 2, one crossing the y‑axis at (0,4) (also through (1,6), (−2,0)) and the other at (0,8) (also through (1,10), (−4,0)).