In this paper, we thoroughly investigated the EM's behavior in overspecified two-component Mixed Linear Regression (2MLR) models. We rigorously characterized the EM estimates for both regression parameters and mixing weights by providing the approximate dynamic equations for the evolution of EM estimates and establishing the convergence guarantees for the final accuracy, time complexity, and sample complexity at population and finite-sample levels, respectively. Additionally, our novel analysis sharpens bounds for statistical error, time complexity, and sample complexity with fixed sufficiently balanced mixing weights. Furthermore, we discussed the differences between results of 2MLR and 2GMM, and extended our analysis from the overspecified setting to the finite low SNR regime.