problem: Find the ordered pair $(x,y)$ if
  
  \begin{align*}
  x+y&=(3-x)+(3-y),\\
  x-y &=(x-2)+(y-2).
  \end{align*}
solution: Adding the equations, we get  $$2x=2\Rightarrow x=1.$$ Substituting this into the first equation, we get $$1+y=5-y\Rightarrow y=2.$$ Thus the ordered pair is $\boxed{(1,2)}$.