Question

Which of these graphs shows that the linear system y=−x+6
𝑦
=
−
𝑥
+
6
and 3x+3y=18
3
𝑥
+
3
𝑦
=
18
has an infinite number of solutions?

Answer 1

The second equation simplifies to x + y = 6, so y = −x + 6. That is exactly the same as the first equation, so the two lines coincide. The graph that shows the same line twice (the line through (0,6), (6,0), (3,3), etc.) is the one that indicates an infinite number of solutions.