In this paper, we consider a relay-assisted uplink non-orthogonal multiple access (NOMA) system. In this system, two radio frequency (RF) users are grouped for simultaneous transmissions, over each resource block, to an intermediate relay. The relay then forwards the amplified version of the users' aggregated signals, in the presence of multiuser interference, to a relatively far destination. In order to cope with the users' ever-increasing desire for higher data rates, a high-throughput free-space optics (FSO) link is employed as the relay-destination backhaul link. It is assumed that the FSO backhaul link is subject to Gamma-Gamma turbulence with pointing error. Also, a Rayleigh fading model is considered for the user-relay access links. Under these assumptions, we derive closed-form expressions for the outage probability and tractable forms, involving only one-dimensional integrals, for the ergodic capacity. Moreover, the outage probability and ergodic capacity analysis are extended to the conventional RF-backhauled systems in the presence of multiuser interference to both relay and destination nodes, and Rician fading for the relay-destination RF link. Our results reveal the superiority of FSO backhauling for high-throughput and high-reliability NOMA systems compared to RF backhauling. This work can be considered as a general analysis of dual-hop uplink NOMA systems as well as the first attempt to incorporate power-domain NOMA in mixed RF-FSO systems.