http://www.physicsforums.com/showthread.php?t=57000

 system of linear congruences
the system:

24x + 11y= 4 (mod 35)
5x + 7y= -13 (mod 35)

is solved to get:

-113y= 111 (mod 35)
113x= 171 (mod 35)

which gives: (17,8).

should there not be more solutions?