Answer
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} 2 \\ 3 \end{bmatrix} $
Work Step by Step
We will write the system of equations as follows:
$\begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} 5 \\ -1 \end{bmatrix} $
Next, we will find the inverse of the left matrix factor as follows:
$\dfrac{1}{(1)(-1)-(1)(1)}\begin{bmatrix} -1 & -1 \\ -1 & 1 \end{bmatrix} $
This yields to: $\begin{bmatrix} 1/2 & 1/2 \\ 1/2 & -1/2 \end{bmatrix} $
Therefore, the value of $x,y$ can be calculated as:
$\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} 1/2 & 1/2 \\ 1/2 & -1/2 \end{bmatrix} \begin{bmatrix} 5 \\ -1 \end{bmatrix} $
or, $\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} (1/2)(5)+(1/2)(-1) \\ (1/2)(5) - (1/2)(-1) \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix} $
Hence, our result is:
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} 2 \\ 3 \end{bmatrix} $
