problem: If $725x + 727y = 1500$ and $729x+ 731y = 1508$, what is the value of $x - y$ ?
solution: Subtracting the two equations gives: \begin{align*}
  (729x+731y)-(725x+727y) &= 1508-1500\\
  \Rightarrow\qquad 4x+4y &= 8\\
  \Rightarrow\qquad x+y &= 2.
  \end{align*}Multiplying this equation by 725 and subtracting this equation from $725x+727y=1500$ gives \begin{align*}
  (725x+727y) - 725(x+y) &= 1500-725(x+y) \implies \\
  2y &= 50.
  \end{align*}So we can write $x-y$ as $(x+y) - 2y$, which equals  $2 - 50 = \boxed{-48}$.