Two-dimensional shear-wave elastography presents 2-D quantitative shear elasticity maps of tissue, which are clinically useful for both focal lesion detection and diffuse disease diagnosis. Realization of 2-D shear-wave elastography on conventional ultrasound scanners, however, is challenging because of the low tracking pulse-repetition-frequency (PRF) of these systems. Although some clinical and research platforms support software beamforming and plane-wave imaging with high PRF, the majority of current clinical ultrasound systems do not have the software beamforming capability, which presents a critical challenge for translating the 2-D shear-wave elastography technique from laboratory to clinical scanners. To address this challenge, this paper presents a time-aligned sequential tracking (TAST) method for shear-wave tracking on conventional ultrasound scanners. TAST takes advantage of the parallel beamforming capability of conventional systems and realizes high-PRF shear-wave tracking by sequentially firing tracking vectors and aligning shear wave data in the temporal direction. The comb-push ultrasound shear elastography (CUSE) technique was used to simultaneously produce multiple shear wave sources within the field-of-view (FOV) to enhance shear wave SNR and facilitate robust reconstructions of 2-D elasticity maps. TAST and CUSE were realized on a conventional ultrasound scanner. A phantom study showed that the shear-wave speed measurements from the conventional ultrasound scanner were in good agreement with the values measured from other 2-D shear wave imaging technologies. An inclusion phantom study showed that the conventional ultrasound scanner had comparable performance to a state-of-the-art shear-wave imaging system in terms of bias and precision in measuring different sized inclusions. Finally, in vivo case analysis of a breast with a malignant mass, and a liver from a healthy subject demonstrated the feasibility of using the conventional ultrasound scanner for in vivo 2-D shear-wave elastography. These promising results indicate that the proposed technique can enable the implementation of 2-D shear-wave elastography on conventional ultrasound scanners and potentially facilitate wider clinical applications with shear-wave elastography.