Substitution Method

The substitution method involves solving one of the equations for one of the variables and substituting the resulting expression into the other equation. This is generally the method of choice when one of the equations is already solved for one of the variables. In a non-linear system of equations in might be the only method of solution so it is an important technique even if it is not your preferred method of solving systems of linear equations.

 

Example:

Solve the following system of equations using the substitution method.

 

y = 2x - 5

3x - 2y = 6

Move your mouse over the equations to see the solution or watch the video solution.

 

 

NOTE: When solving an equation with the substitution method, if you end up with a true expression such as 0 = 0, the system is a dependent system (coinciding lines) and has infinitely many solutions. If you end up with a false statement, such as 2 = 5, the system is inconsistent (parallel lines) and has no solution.