Let (x,y,z) ∈ ℂ³. In this paper we shall study the solvability of singular first order partial differential equations of nilpotent type by the following typical example: $Pu(x,y,z):=(y{\partial }_x-z{\partial }_y)u(x,y,z)=f(x,y,z){\in }_{x,y,z}$, where $P=y{\partial }_x-z{\partial }_y{:}_{x,y,z}{\to }_{x,y,z}$. For this equation, our aim is to characterize the solvability on ${}_{x,y,z}$ by using the Im P, Coker P and Ker P, and we give the exact forms of these sets.