# How do you write the augmented matrix for the system of linear equations 4x-3y=-5, -x+3y=12?

Aug 8, 2017

The solution is $\left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\begin{matrix}\frac{28}{3} \\ \frac{43}{9}\end{matrix}\right)$

#### Explanation:

We perform the Gauss Jordan elimination with the augmented matrix

$M = \left(\begin{matrix}4 & - 3 & : & - 5 \\ - 1 & 3 & : & 12\end{matrix}\right)$

We perform the row operations

$R 2 \leftarrow 4 R 2 + R 1$, $\implies$, $\left(\begin{matrix}4 & - 3 & : & - 5 \\ 0 & 9 & : & 43\end{matrix}\right)$

$R 2 \leftarrow \frac{R 2}{9}$, $\implies$, $\left(\begin{matrix}4 & - 3 & : & - 5 \\ 0 & 1 & : & \frac{43}{9}\end{matrix}\right)$

$R 1 \leftarrow R 1 + 3 R 2$, $\implies$, $\left(\begin{matrix}4 & 0 & : & \frac{28}{3} \\ 0 & 1 & : & \frac{43}{9}\end{matrix}\right)$

$R 1 \leftarrow \frac{R 1}{4}$, $\implies$, $\left(\begin{matrix}1 & 0 & : & \frac{28}{12} \\ 0 & 1 & : & \frac{43}{9}\end{matrix}\right)$