Compute the ordered pair of positive integers $(x,y)$ such that

\begin{align*}
x^y+1&=y^x,\\
2x^y&=y^x+7.
\end{align*}
Question:
Compute the ordered pair of positive integers $(x,y)$ such that

\begin{align*}
x^y+1&=y^x,\\
2x^y&=y^x+7.
\end{align*}
Answer:
Let's think step by step.

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(2,3)
Compute the ordered pair of positive integers $(x,y)$ such that

\begin{align*}
x^y+1&=y^x,\\
2x^y&=y^x+7.
\end{align*}
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