Integers $x$ and $y$, with $x>y$, satisfy $x+y=7$ and $x y=12$.

Integers $m$ and $n$, with $m>n$, satisty $m+n=13$ and $m^{2}+n^{2}=97$.

If $A=x-y$ and $B=m-n$, determine the value of $A-B$.
If $x$ and $y$ are integers with $x>y$ and $x+y=7$ and $x y=12$, then $x=4$ and $y=3$, so $A=x-y=1$. (We can check that there are no other solutions.)

If $m$ and $n$ are integers with $m>n$ and $m+n=13$ and $m^{2}+n^{2}=97$, then $m=9$ and $n=4$, so $B=m-n=5$. (We can check that there are no other solutions.)

Therefore, $A-B=1-5=-4$.

ANSWER: -4