Summary: System with five equations, two variables. Inconsistent, overdetermined. Null space of coefficient matrix has dimension 0. Coefficient matrix identical to that of Archetype G, constant vector is different.
Definition:\begin{align*} 2x_1 + 3x_2 &= 5 \\ -x_1 + 4x_2 &= 6 \\ 3x_1 +10x_2 &= 2 \\ 3x_1 - x_2 &= -1 \\ 6x_1 + 9x_2 &= 3 \end{align*}