Why can I solve an impossible equation using linear algebra?

I am currently learning matlab and linear algebra side by side and I stumbled upon this example from mathworks

A = [1 2 0; 0 4 3];
b = [8; 18];
x = A\b

x = 3×1

     0
4.0000
0.6667

which in my mind translates to

$$ A = \left[ \begin{matrix} 1 & 2 & 0 \\ 0 & 4 & 3 \end{matrix}\right] B = \left[ \begin{matrix} 8 \\ 18 \end{matrix}\right] x = \left[ \begin{matrix} a \\ b \\ c \end{matrix}\right] $$

$$ Ax = \left[ \begin{matrix} 1 & 2 & 0 \\ 0 & 4 & 3 \end{matrix}\right] \times \left[ \begin{matrix} a \\ b \\ c \end{matrix}\right] = \left[ \begin{matrix} a + 2b \\ 4b + 3c \end{matrix}\right] $$

which boils down to $$ \left[ \begin{matrix} a + 2b \\ 4b + 3c \end{matrix}\right] = \left[ \begin{matrix} 8\\ 18 \end{matrix}\right] \Rightarrow \begin{matrix}a + 2b = 8 \\4b + 3c = 18\end{matrix} $$

which is an equation with 3 unknown (a, b and c) with two equations, which is impossible! Yes there is a solution $$ x = \left[ \begin{matrix} 0 \\ 4 \\ 2/3 \end{matrix}\right] $$

How can I solve an impossible equation (three unknown and two equations) using linear algebra?

from Hot Weekly Questions - Mathematics Stack Exchange