Find the ordered pair $(x,y)$ if

\begin{align*}
x+y&=(3-x)+(3-y),\\
x-y &=(x-2)+(y-2).
\end{align*}
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the ordered pair $(x,y)$ if

\begin{align*}
x+y&=(3-x)+(3-y),\\
x-y &=(x-2)+(y-2).
\end{align*}
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(1,2)
Find the ordered pair $(x,y)$ if

\begin{align*}
x+y&=(3-x)+(3-y),\\
x-y &=(x-2)+(y-2).
\end{align*}
train