If this is simply a pair of simultaneous linear equations, the solution is fairly straight forward.
Multiply the first equation by b and the second by a to give
abx + b^2y = b(a-b)
abx-a^2y=a(a=b)
(a^2+b^2)y=b(a-b)-a(a+b)=ba-b^2-a^2-ab=-(a^2+b^2) and y=-1
Plug y=-1 into the first equation to get ax-b=a-b and x=1
Plug these values of x and y into the second equation to check.
If there is some other meaning to the questions, then all bets are off!
