Section 2.2 – Solving Systems of Linear Equation I 1Section 2.2 Solving Systems of Linear Equations I As you may recall from College Algebra, you can solve a system of linear equations in two variables easily by applying the substitution or addition method. Since these methods become tedious when solving a large system of equations, a suitable technique for solving such systems of linear equations of any size is the Gauss-Jordan elimination method. This method involves a sequence of operations on a system of linear equations to obtain at each stage an equivalent system. The Gauss-Jordan elimination method is complete when the original system has been transformed so that it is in a certain standard form from which the solution can be easily read. Augmented MatricesMatricesare rectangular arrays of numbers. We will use these to solve systems of equation in 2 or more variables. Example: Given 222758322642=++−=++=++zyxzyxzyx.