Flash calculations are used extensively in computer-aided process simulation programs. Inherent to flash calculations is the determination of the vapor liquid split. Currently, to calculate the vapor liquid split, the Rachford-Rice equation is the most accepted method. In this work, it is shown that the Rachford-Rice equation can be posed as a generalized eigenvalue problem, where each eigenvalue of the resulting system is exactly a root of the Rachford-Rice equation. In this way, an ad hoc strategy based on linear algebra is proposed for finding the vapor liquid split. The main advantage of the proposed strategy is that the resulting linear system has an almost-diagonal structure and generates a discrepancy function with a more linear shape than that of the Rachford-Rice equation. In this way, the solution of the system is simple and computationally inexpensive. Numerical experiments show the reliability of the proposed solution strategy for calculating the vapor liquid split.