Systems of singular integral equations appear in many branches of scientific fields [1–6], such as microscopy, seismology, radio astronomy, electron emission, atomic scattering, radar ranging, plasma diagnostics, X-ray radiography, and optical fiber evaluation. Studies of systems of singular integral equations have attracted much concern in applied sciences. The use of computer symbolic systems such as Maple and Mathematica facilitates the tedious work of computation. The general ideas and the essential features of these systems are of wide applicability.