What does the substitution method involve when solving systems of equations?

The substitution method is a systematic approach used to solve systems of equations. It involves taking one of the equations and isolating one of the variables, allowing you to express it in terms of the other variable. By replacing that variable in the remaining equation with its equivalent expression, you can turn the system into a single-variable equation. This process simplifies finding the solution by reducing the complexity of the system. Once you solve for the isolated variable, you can back-substitute to find the value of the other variable.

This method is particularly useful when one of the equations is easy to manipulate, making it straightforward to express one variable in terms of the other. The clarity of this approach allows for efficient problem-solving in both linear and nonlinear systems.