# How do you solve x-y=6 and 2x + 3y =2 using matrices?

Sep 28, 2017

The solution is $\left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\begin{matrix}4 \\ - 2\end{matrix}\right)$

#### Explanation:

Let's perfom the Gauss-Jordan elimination on the augmented matrix

The augmented matrix is

$\left(\begin{matrix}1 & - 1 & | & 6 \\ 2 & 3 & | & 2\end{matrix}\right)$

Let`s perform the row operations

$R 2 \leftarrow \left(R 2 - 2 R 1\right)$

$\left(\begin{matrix}1 & - 1 & | & 6 \\ 0 & 5 & | & - 10\end{matrix}\right)$

$R 2 \leftarrow \frac{R 2}{5}$

$\left(\begin{matrix}1 & - 1 & | & 6 \\ 0 & 1 & | & - 2\end{matrix}\right)$

$R 1 \leftarrow \left(R 1 + R 2\right)$

$\left(\begin{matrix}1 & 0 & | & 4 \\ 0 & 1 & | & - 2\end{matrix}\right)$

The solution is $\left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\begin{matrix}4 \\ - 2\end{matrix}\right)$

Oct 13, 2017

$x = 4 , y = - 2$

#### Explanation:

$x = 4 , y = - 2$