Let a,b,c,d,u,v  be integers, if the system of equations ax+by=u , cx+dy=v  has a unique solution in integers, then

ad−bc  may or may not be ±1 . Surely ad−bc≠0 . As an example consider the equations 2x−3y=7 , 3x+y=5  which have integral solution but ad−bc=2+9=11 .Note that the converse is true i.e., if ad−bc=1  or −1 , the given system has integral solutions.