Div is simply the integer part of the result of a division, while modulo (mod) is the positive remainder after division. When the remainder is negative add the divisor to make it positive.
The two equations simplify:
5x+4y=1; 4x+2y=0 or 2x+y=0 and y=-2x. Substitute for y in the first equation: 5x-8x=1, -3x=1, so x=-1/3 and y=2/3.
Solution: x=-1/3 and y=2/3.