The solution of the two-dimensional polynomial equationb(z_1,z_2)f(z_1,z_2) + a(z_1,z_2)g(z_1,z_2) = h(z_1,z_2)

This paper proposes an algorithm for finding the solution of the two-dimensional (2-D) Diophantine equation. The solution, when it exists, is not unique. However, the solution with minimal degrees is unique and can be achieved by this algorithm. An example is given to illustrate the procedure. The method is also applied to determine if two polynomial functions are zero coprime (ZC) or not. They can be readily extended to three- or higher dimensional cases.