# How do you write the augmented matrix for the system of linear equations 7x+4y=22, 5x-9y=15?

Aug 1, 2017

The solution is $\left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\begin{matrix}\frac{258}{83} \\ \frac{5}{83}\end{matrix}\right)$

#### Explanation:

The equations are

$7 x + 4 y = 22$

$5 x - 9 y = 15$

The augmented matrix is

$\left(\begin{matrix}7 & 4 & | & 22 \\ 5 & - 9 & | & 15\end{matrix}\right)$

$R 2 \leftarrow 7 R 2 - 5 R 1$

$\left(\begin{matrix}7 & 4 & | & 22 \\ 0 & - 83 & | & - 5\end{matrix}\right)$

$R 2 \leftarrow \frac{R 2}{- 83}$

$\left(\begin{matrix}7 & 4 & | & 22 \\ 0 & 1 & | & \frac{5}{83}\end{matrix}\right)$

$R 1 \leftarrow R 1 - 4 R 2$

$\left(\begin{matrix}7 & 0 & | & \frac{1806}{83} \\ 0 & 1 & | & \frac{5}{83}\end{matrix}\right)$

$R 1 \leftarrow \frac{R 1}{7}$

$\left(\begin{matrix}1 & 0 & | & \frac{258}{83} \\ 0 & 1 & | & \frac{5}{83}\end{matrix}\right)$