Question

Which of these graphs shows that the linear system 3x−2y=12
3
𝑥
−
2
𝑦
=
12
and −6x+4y=−24
−
6
𝑥
+
4
𝑦
=
−
24
has an infinite number of solutions?

Answer 1

The second equation is -2 times the first, so they are the same line. Both reduce to y = (3/2)x − 6, so the system is dependent and has infinitely many solutions (every point on that line).

So pick the graph that shows one line (or two coincident/overlapping lines) with slope 3/2 and y‑intercept −6 (points: (0,−6), (2,−3), (4,0)).