Archetype D is the system of $m=3$ equations in $n=4$ variables, \begin{align*} 2x_1 + x_2 + 7x_3 - 7x_4 &= 8 \\ -3x_1 + 4x_2 -5x_3 - 6x_4 &= -12 \\ x_1 +x_2 + 4x_3 - 5x_4 &= 4 \end{align*} and the solution $x_1 = 0$, $x_2 = 1$, $x_3 = 2$, $x_4 = 1$ can be checked easily by substitution. Having been handed this solution, we know the system is consistent. This, together with $n>m$, allows us to apply Theorem CMVEI and conclude that the system has infinitely many solutions.