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

They are multiples of each other (6x+4y = 2(3x+2y)), so they represent the same line. The graph that shows an infinite number of solutions is the one where the two lines coincide (overlap exactly).

That line has equation 3x+2y=12, so y = −(3/2)x + 6 and intercepts (0,6) and (4,0). Pick the graph showing a single line through (0,6) and (4,0) (or two overlapping lines).