Possible Duplicate:
Proving two gcd's equal
Let $a,b,c,d,x,y$ be integers with $\gcd(x,y)=1$ and $ \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad-bc = 1. $ I have come across the assertion that $(ax+by)$ and $(cx+dy)$ must be relatively prime, but I don't see why.
$gcd(x,y)=1$ means there are $C,D$ such that $Cx+Dy=1$
I want to find $A,B$ such that $A(ax+by) + B(cx+dy) = 1.$
I've tried expanding and regrouping the terms in the LHS in different ways to try to use what I've got, but I'm stuck.
Can someone please help me out?