In this study, we have performed simultaneous solutions of light and radial velocity curves of two eclipsing binary systems, V566 Oph and V972 Her. We observed both systems spectroscopically with a very recently installed spectrograph on the 40 cm telescope, T40, located in Ankara University Kreiken Observatory (AUKR), for the first time. We made use of the photometric data from the Hipparcos satellite for V972 Her, while we obtained the photometric observations of V566 Oph by using the 35 cm telescope, T35, located also in our observatory campus. We derived the absolute parameters for both systems and discussed their evolutionary states. In addition to the simultaneous analysis, we have also analyzed the change in mid-eclipse times for V566 Oph, and found cyclic variations, for which we have discussed light-time effect and magnetic activity as their potential origin, superimposed on a secular change due to a mass transfer between the components of the binary.