5x +  6y = 3
-25x - 30y = 6

If you try to solve the system by multiplying the first
equation through by 5 you get

 25x + 30y = 15
-25x - 30y =  6

Then when you add the equations vertically term by term:

 25x + 30y = 15
-25x - 30y =  6
---------------
        0y = 21

And there can be no possible value for y, because there is
no value for y that you can multiply by 0 and get 21, because
you'll always get 0 instead.

So the system has no solution because the system is inconsistent.
That is if you draw their graphs, they do not intersect to give
a solution because they are parallel.  Here are their graphs: 



Edwin