Solving algebraic equations using modeling techniques could ease up the process greatly, it can help for effecient and optimal time . in essence a system of equations could be considered a model. and then this model can refactored using simplification rules( like for example make all the terms in the left hand side, and reduce the number of operators by factoring out common terms) .
this really looks like we are refactoring the equations, or the model, its eventually the same equation. but this refactoring is systematic and will lead to reveal the shortest way to solve this model .