This study investigates boundary value problems for the Bitsadze equation defined on a quarter plane. The Bitsadze equation, a fundamental partial differential equation in the theory of analytic functions, often appears in complex analysis and mathematical physics. Despite extensive research on boundary value problems in various domains, the quarter plane case remains less explored. We consider specific boundary conditions that are either Dirichlet or Schwarz types on the respective edges of the quarter plane. By employing the method of integral transforms, we reduce the problem to a system of integral equations. The solvability of these equations is analyzed using analysis techniques. We further explore the uniqueness and existence of the solutions under different boundary conditions. In case of Upper half plane these problems are also studied. In case of first order partial differential equations, Gauss theorem and the Cauchy Pompeiu formulas are used to find fundamental solutions of these equations.