Systems comprised of Cognitive Radio Networks (CRN) have been gaining attention in the current literature, given their ability to reduce spectrum scarcity by reusing parts of the spectrum band, while at the same time ensuring a minimum Quality of Service (QoS) margin. In this regard, it becomes important to consider the CRN's usage of multiple access protocols. In this paper, we consider a CRN with the Slotted Aloha protocol, and in order to improve the system's performance, we also proposed the use of an adaptive modulation technique. Finding the optimum switching points between neighboring modulations is a key issue of the adaptive modulation system. Thus, we investigated the optimum switching points through the maximum throughput criterion for a primary and secondary network considering the Capture Effect and the interference between primary and secondary users.