Answer
$x=1; y= 7; z=-9$
Work Step by Step
A system of equations can be written in the form: $AX=B$
where $B= \begin{bmatrix} x \\ y \\ z \end{bmatrix}$
When there exists an inverse of a matrix, the following relationship is true:
$A A^{-1} = I$
Thus, $X=A^{-1} B = \begin{bmatrix} 1&1&1 \\ 3 & 5 & 4 \\ 3&6& 5 \end{bmatrix} \begin{bmatrix} -1 \\ 2 \\ 0 \end{bmatrix} =\begin{bmatrix} 1 \\ 7 \\-9 \end{bmatrix}$
So, $X= \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix}1 \\ 7 \\-9 \end{bmatrix}$
Therefore, $x=1; y= 7; z=-9$
