Will graphs for these equations show parallel lines? Explain.

y=6x+1

y=6x-5

Yes these lines are parallel. They will never cross so there are no solutions to this system.

The reason why is because the two slopes for the equations are both 6 each. The equations are in y = mx+b form where m is the slope. The y intercepts are different (1 for the first; - 5 for the second). So those two pieces of info lead to non-intersecting parallel lines.