2016 AMC 12A Problems/Problem 16
The graphs of and are plotted on the same set of axes. How many points in the plane with positive -coordinates lie on two or more of the graphs?
Setting the first two equations equal to each other, .
Solving this, we get and .
Similarly with the last two equations, we get and .
Now, by setting the first and third equations equal to each other, we get .
Pairing the first and fourth or second and third equations won't work because then .
Pairing the second and fourth equations will yield , but since you can't divide by , it doesn't work.
After trying all pairs, we have a total of solutions