How do you solve a system of equations using the substitution method?

The substitution method for solving a system of equations involves isolating one variable in one of the equations and then substituting this expression into the other equation. This approach simplifies the system into a single equation with one variable, which can then be solved directly.

For example, if you have two equations, you might solve the first one for ( x ) in terms of ( y ). Then, you would take this expression for ( x ) and substitute it into the second equation. This method allows you to work with just one variable at a time, making it easier to find the solution to the system.

This process contrasts with other methods such as elimination, where variables are removed through addition or subtraction without direct substitution, or graphing, where visual representation is used to find intersection points of lines. Additionally, calculating the determinant is more aligned with methods for checking the existence and nature of solutions rather than directly solving for variable values. Thus, the substitution method specifically focuses on solving for variables by substituting expressions, making the correct answer the third option.