In this work, we present the performance analysis of a dual-branch transmission system composed of a direct radio frequency (RF) link and a dual-hop relay composed of asymmetric RF and free-space optical (FSO) links and compare it without having a direct RF path to see the effects of diversity on our system. The FSO link accounts for pointing errors and both types of detection techniques (i.e. indirect modulation/direct detection (IM/DD) as well as heterodyne detection). The performance is evaluated under the assumption of selection combining diversity scheme. RF links are modeled by Rayleigh fading distribution whereas the FSO link is modeled by a unified Gamma-Gamma fading distribution. Specifically, we derive new exact closed-form expressions for the cumulative distribution function, probability density function, moment generating function, and moments of the end-to-end signal-to-noise ratio of these systems in terms of the Meijer's G function. We then capitalize on these results to offer new exact closed-form expressions for the outage probability, higher-order amount of fading, average error rate for binary and M-ary modulation schemes, and ergodic capacity, all in terms of Meijer's G functions. All our new analytical results are also verified via computer-based Monte-Carlo simulations.