How many intersections are there of the graphs of the equations below? 1/2x + 5y = 6 3x + 30y = 36

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.