Question 39
Find all positive real-valued solutions to
$$
\begin{cases} x - y + \frac{1}{z} = 2013, \\ y - z + \frac{1}{x} = 2013, \\ z - x + \frac{1}{y} = 2013. \end{cases}
$$
$$
\begin{cases} x - y + \frac{1}{z} = 2013, \\ y - z + \frac{1}{x} = 2013, \\ z - x + \frac{1}{y} = 2013. \end{cases}
$$