Both sides use the same pair to take the partial derivative of x.

fu(x-y，y-z，z-x) -fv(x-y，y-z，z-x)dz/dx +fw(x-y，y-z，z-x)(dz/dx- 1) =0

At the same time, the derivative of y is obtained.

-fu(x-y，y-z，z-x) -fv(x-y，y-z，z-x)( 1-dz/dy) +fw(x-y，y-z，z-x)dz/dy =0

So dz/dx and dz/dy have two equations, which can be added after solving dz/dx and dz/dy respectively.