As this is an equation with two variables there are an infinite number of possible solutions.
for example x = 1 y = -1/4
or x = 0 y = -2
We can consider equation above as a Diofantic equation
A diofantic equation is a particular case of general equation where solutions are allways integers
We consider by now the homogeneus case
Now the complete case solutions are obtained
The solution is unique if and only if GCD(A,B) divide to C