Find the number of ordered triples $(x,y,z)$ of real numbers that satisfy
\begin{align*}
x + y - z &= 0, \\
xz - xy + yz &= 27, \\
xyz &= 54.
\end{align*}
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the number of ordered triples $(x,y,z)$ of real numbers that satisfy
\begin{align*}
x + y - z &= 0, \\
xz - xy + yz &= 27, \\
xyz &= 54.
\end{align*}
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
3
Find the number of ordered triples $(x,y,z)$ of real numbers that satisfy
\begin{align*}
x + y - z &= 0, \\
xz - xy + yz &= 27, \\
xyz &= 54.
\end{align*}
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