Item1.2.5.1.c

The augmented matrix and its reduced row echelon form are

\begin{equation*} \left[\begin{array}{rrrrr} -2 \amp 3 \amp 0 \amp 2 \amp 7 \\ -1 \amp 4 \amp 1 \amp 3 \amp 9 \\ 3 \amp 0 \amp 2 \amp 2 \amp -1 \\ 1 \amp 5 \amp 4 \amp 7 \amp 8 \end{array}\right] \sim \left[\begin{array}{rrrrr} 1 \amp 0 \amp 0 \amp 0 \amp 1 \\ 0 \amp 1 \amp 0 \amp 0 \amp 3 \\ 0 \amp 0 \amp 1 \amp 0 \amp -2 \\ 0 \amp 0 \amp 0 \amp 1 \amp 0 \end{array}\right]\text{,} \end{equation*}

which shows that there is a single solution \((1,3,-2,0)\text{.}\) Every variable is a basic variable.

in-context