Question

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

Answer 1

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.