Gaussian elimination

Procedure is as following

1. Obtain augmented matrix $\left[\begin{array}{c}A|b\end{array}\right]$
2. Apply elementary row operations to the augmented matrix until you reach $\left[\begin{array}{c}E|d\end{array}\right]$ where $E$ is in row echelon form.
3. The columns of $E$ that do not contain a leading $1$ correspond to the free variables
4. The columns of $E$ that contain leading $1$‘s should be expressed in the free variables.