Solutions to the System of Operator EquationsA1X=C1,XB2=C2, andA3XB3=C3on HilbertC*-Modules

We study the solvability of the system of the adjointable operator equations A1X=C1, XB2=C2, and A3XB3=C3 over Hilbert C*-modules. We give necessary and sufficient conditions for the existence of a solution and a positive solution of the system. We also derive representations for a general solution and a positive solution to this system. The above results generalize some recent results concerning the equations for operators with closed ranges