##### Item1.2.5.5.d

This is false. The reduced row echelon form of the augmented matrix could look like

\begin{equation*} \left[\begin{array}{rr|r} 1 \amp 0 \amp -3 \\ 0 \amp 1 \amp 4 \\ 0 \amp 0 \amp 0 \\ \end{array}\right]\text{.} \end{equation*}

In this case, there are three equations in two unknowns, and the system has exactly one solution.

in-context