Consider the system $Ax = b$ where $A = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{pmatrix}$ and $b = \begin{pmatrix} 6 \\ 10 \\ 18 \end{pmatrix}$. Find the value of $x_3$.