**5.3.1 Encoding systems into matrix equations**

\( \begin{cases} ax+by=c\\
dx+ex=f\end{cases} \iff \begin{pmatrix}
a & b\\
d & e
\end{pmatrix}\begin{pmatrix}
x\\
y
\end{pmatrix}=\begin{pmatrix}
c\\
f
\end{pmatrix} \)**coefficient matrix** is \( \begin{pmatrix} a & b\\ d & e \end{pmatrix} \), **augmented matrix** is \( \left( \begin{matrix} a & b\\ d & e \end{matrix} \middle| \begin{matrix} c\\ f \end{matrix} \right) \)