When you deal with systems of three equations with three variables, you extend the addition and multiplication activities you perform when you work with systems of two equations with two variables. The goals and procedures remain the same. Your task is to move through the equations, multiplying and adding so that you can express the equations so that they identify the values of the constituent variables.
To examine how to work with a system of three equations with three variables, consider this system:
|2x - 4y + 6z = 22||A|
|4x + 2y - 3z = 4||B|
|3x + 3y - z = 4||C|
To make it easier to identify the equations, you can associate them with letters of the alphabet. As you go, the letters allow you to continue to identify the equations ...