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In this paper, we consider the widely popular structure-preserving models used to describe the dynamic behavior of multimachine power systems. These models consist of differential-algebraic equations, where the algebraic constraints stem from the power flow balance between generators, loads, and lines. Our main contribution is the explicit computation of a solution for these algebraic equations under the assumption that the loads are constant impedances. This result is of interest for transient stabilization problems where, to estimate the domain of attraction of a given control law, it is sometimes necessary to explicitly solve the algebraic constraints. Besides this application, we believe this result may be of interest in other problems of power systems analysis.