The number of intersections of the graphs of the equations is the number of solutions of the system.
The system is:
(1/2)x + 5y = 6
3x + 30y = 36
If you multiply the first equation times 6 you get to:
6(x/2) + 6(5y) = 6(6)
=> 3x + 30y = 36
And that is the same second equation, that means that the system is indetermined.
Being the two equations the same, the two graphs are superposed.
So there are infinite intersections.
