Answer
$x=3; y= 8; z=-11$
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, $X=A^{-1} B = \begin{bmatrix} 1&1&-1 \\ -3 & 2 &1 \\ 3&-3& 2 \end{bmatrix} \begin{bmatrix} 0 \\ 5 \\ 2 \end{bmatrix} =\begin{bmatrix} 3 \\ 8 \\-11 \end{bmatrix}$
So, $X= \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix}3 \\ 8 \\-11 \end{bmatrix}$
Therefore, $x=3; y= 8; z=-11$
