System of equations with three equations

Most systems of equations problems only involve two equations, but occasionally they’ll include three equations, often in the form of a word problem. For these problems, students need to isolate two different variables in two of the equations. These then need to be substituted in for each other in the 3rd equation.

The main key is that at some point all of the variables in the equation will need to be substituted or eliminated until only one variable and a constant remain.

For example:

3x + 2y − z = 6

 − 2x + 2y + z = 3

x + y + z = 4