$$ 
\begin{bmatrix}
1 & 2 & 3\\
4 & 5 & 6
\end{bmatrix}
$$
To write a system of equations as a matrix, you use the coefficients of each term. The solutions for each equation might be written with a bar separating:

$$ 
\begin{bmatrix}
1 & 2 & 3|4\\
4 & 5 & 6|5
\end{bmatrix}
$$