Question

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

Answer 1

Both equations simplify to the same line:

- First: −2x + y = 6 → y = 2x + 6.
- Second: 4x − 2y = −12 → divide by 2 → 2x − y = −6 → y = 2x + 6.

So the graph that shows an infinite number of solutions is the one where the two lines coincide (a single line with slope 2 and y‑intercept 6 — e.g. through (0,6) and (−3,0)).