The augmented matrix does not contain a row in which the only nonzero entry appears in the last column. Therefore, this system of equations must be consistent.

Convert the augmented matrix into a system of equations.

\(x_1-2x_2=6\)

0=0

Solve for the leading entry for each individual equation. Determine the free variables, if any.

\(x_1=6+2x_2\)

\(x_2\), free

Parameterize the free variables.

\(x_1=6+2t\)

\(x_2=t\)

Write the solution in vector form.

\(x=\begin{bmatrix}6 \\0 \end{bmatrix}+t\begin{bmatrix}2 \\1 \end{bmatrix}\)