We present two events to study the driving mechanism of extreme-ultraviolet (EUV) waves that are not associated with coronal mass ejections (CMEs), by using high-resolution observations taken by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. Observational results indicate that the observed EUV waves were accompanied by flares and coronal jets, but not the CMEs that were regarded as drivers of most EUV waves in previous studies. In the first case, it is observed that a coronal jet is ejected along a transequatorial loop system at a plane-of-the-sky (POS) speed of 335 +/- 22 km s(-1); in the meantime, an arc-shaped EUV wave appeared on the eastern side of the loop system. In addition, the EUV wave further interacted with another interconnecting loop system and launched a fast propagating (QFP) magnetosonic wave along the loop system, which had a period of 200 s and a speed of 388 +/- 65 km s(-1), respectively. In the second case, we observed a coronal jet that ejected at a POS speed of 282 +/- 44 km s(-1) along a transequatorial loop system as well as the generation of bright EUV waves on the eastern side of the loop system. Based on the observational results, we propose that the observed EUV waves on the eastern side of the transequatorial loop systems are fast-mode magnetosonic waves and that they are driven by the sudden lateral expansion of the transequatorial loop systems due to the direct impingement of the associated coronal jets, while the QFP wave in the fist case formed due to the dispersive evolution of the disturbance caused by the interaction between the EUV wave and the interconnecting coronal loops. It is noted that EUV waves driven by sudden loop expansions have shorter lifetimes than those driven by CMEs.