Multi-agent systems' cooperation to achieve global goals is usually limited by sensing, actuation, and communication issues. At the local level, continuous measurement and actuation is only approximated by the use of digital mechanisms that measure and process information in order to compute and update new control input values at discrete time instants. Interaction with other agents takes place, in general, through a digital communication channel with limited bandwidth where transmission of continuous-time signals is not possible. This technical note considers the problem of consensus (or synchronization of state trajectories) of multi-agent systems that are described by general linear dynamics and are connected using undirected graphs. The proposed event-triggered consensus protocol not only avoids the need for continuous communication between agents but also provides a decentralized method for transmission of information in the presence of time-varying communication delays, where each agent decides its own broadcasting time instants based only on local information. This method gives more flexibility for scheduling information broadcasting compared to periodic and sampled-data implementations.