This study investigates an alternative to the commonly used concentration table method for describing chemical equilibria in General Chemistry. The concentration table method is arguably the single most difficult concept for students in this course. The difficulties arise from the number of simplifying assumptions that need to be made. Furthermore, once the problem has been simplified, a significant amount of time is often required for algebraic manipulations, which students in General Chemistry find difficult. As discussed in this paper, it is possible to deal with equilibrium in a more contemporary, holistic approach, where equilibrium expressions, charge, and mass balance equations are solved simultaneously. Such methods reduce the number of assumptions that need to be made to solve a given problem, and when solved using a symbolic computer algebra program, provide a reduction in the amount of work required to reach a numerical solution. Also, since multiple equilibrium reactions are no more difficult to solve than single reactions, students gain a more complete understanding of chemical equilibrium systems. In this study, we present preliminary results from a pilot study in which several different sections in our General Chemistry course are taught using the systematic method. Student understanding of key chemical concepts is monitored and compared to sections which are taught in the traditional manner. Student attitudes are also assessed in terms of perceived difficulties in learning the new method as well as student comfort with working with technology to solve problems. At present, we can state that no significant degradation in student scores is observed. Students in the test sections seem to be performing the same as or slightly above their peers in the standard sections.