Question

Which of the graphs with no solution correctly shows the system of equations y=3x+4
𝑦
=
3
𝑥
+
4
and −3x+y=8
−
3
𝑥
+
𝑦
=
8
?

Answer 1

Rearrange the second equation: −3x + y = 8 → y = 3x + 8. So the two lines are

- y = 3x + 4 (y-intercept 4),
- y = 3x + 8 (y-intercept 8).

They have the same slope (3) but different y-intercepts, so they are parallel and never intersect (no solution). The correct graph is the one that shows two parallel lines with slope 3, one crossing the y-axis at 4 (e.g. through (0,4) and (1,7)) and the other at 8 (e.g. through (0,8) and (1,11)). You can also see no solution algebraically: 3x+4 = 3x+8 → 4 = 8 (contradiction).