# 2016 AMC 12A Problems/Problem 16

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## 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?

## Solution

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