The aggregated visible light communication (VLC) and radio frequency (RF) system, which can be viewed as a heterogeneous multi-input-multi-output system, can improve data rate compared to the conventional RF communication systems. In this paper, we first develop optimal power allocation schemes for the aggregated VLC-RF systems for the single and the multi-light-emitting diode scenarios under different dimming control setups. Moreover, we study the energy efficiency maximization problem of the considered system with the minimum rate requirement, transmitted power constraint, and the dimming control consideration which is non-convex. By using the Dinkelbach-type algorithm, we tackle this problem by solving a sequence of convex problems which converges to the global solution. Finally, the effect of critical parameters, such as total power threshold, dimming level, and bandwidths, are revealed by some selected numerical results.