In this article we find necessary and su cient conditions for the generalized reflexive and antireflexive solution of the system of equations $ax=b$ and $xc=d$ in a ring with involution. As corollaries, among other results, we obtain some recent results from (A. Dajić and J. Koliha, Linear Algebra Appl. (2008)), and Li Fanliang, Hu Xiuyan and Zhang Lei, Acta Math. Scientia 28B(1) (2008)).