# Clever System of Equations Problem

Algebra Level 3

Find all solutions to the system of equations below. $x+y+\frac{x}{y}=19$ $\frac{x(x+y)}{y}=60$ Now, let $(x,y)$ be one solution where $x$ and $y$ are integers. Then, let $(\frac{a}{b},\frac{c}{d})$ be the other solution where $a,b$ and $c,d$ are pairwise coprime positive integers. Find $a+b+c+d+x+y$.

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