What is the purpose of using the substitution method in solving equations?

Using the substitution method is particularly effective when solving a system of equations because it allows one equation to be rewritten in terms of one variable, thus simplifying the process of finding the solution. By isolating one variable, you reduce the complexity of the system, which can make it easier to solve for the values of each variable step by step.

This method is especially useful in situations where the equations are not easily solvable using other methods, such as elimination, or when it's simpler to express one variable in terms of another. Through substitution, you can systematically reduce the problem to a single variable equation, which can then be solved directly.

While the other options provide different interpretations of equation-solving strategies, they do not capture the primary purpose of the substitution method. For instance, making equations more complex contradicts the objective of simplification in solving math problems, and converting to a common base focuses on a different mathematical concept than substitution. Additionally, while finding unique solutions to non-linear equations is a significant aspect of mathematics, the substitution method can be applied more broadly than this specific context.