Answer
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} -3.5423089 \\ -4.3 432684 \end{bmatrix} $
Work Step by Step
We will write the system of equations as follows:
$\begin{bmatrix} 1 & -\sqrt 2 \\ 0.75 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} 2.6 \\ -7 \end{bmatrix} $
Next, the inverse of the left matrix factor by using graphing calculator is as follows:
$\begin{bmatrix} 0.4852814 & 0.6862915 \\ -0.3639610 & 0.4852814 \end{bmatrix} $
Now, the value of $x,y$ can be calculated as:
$\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} 0.4852814 & 0.6862915 \\ -0.3639610 & 0.4852814 \end{bmatrix} \begin{bmatrix} 2.6 \\ -7 \end{bmatrix} $
After matrix multiplication, we get:
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} -3.5423089 \\ -4.3 432684\end{bmatrix} $
Hence, our result is:
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} -3.5423089 \\ -4.3 432684 \end{bmatrix} $
