Solutions using Abel＇s method are developed for the irreversible Michaelis-Menten mechanism that governs enzyme action. From these phase plane solutions, an approximate solution is derived that permits a study of the time course of substrate and complex. Performance of the solutions in the phase plane and in temporal evolution is assessed in comparison to numerical solutions, the quasi-equilibrium and pseudo-steady-state approximations, and the iterative solution obtained by Fraser and co-workers. Both the complete and approximate solutions perform well, especially in parameter regions of most practical interest.