Answer
$x= \dfrac{13}{16}; y=\dfrac{11}{16}; z= -2$
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} 5&-3& -2 & 2 \\ 2 & 2 & -3 & 3 \\ 1 &-7& 8 & -4 \end{bmatrix} \begin{bmatrix} -2 \\ 16 \\ 4 \end{bmatrix} $
So, $X= \begin{bmatrix} x \\ y \\ z \end{bmatrix}= \begin{bmatrix} \dfrac{13}{16} \\ \dfrac{11}{16} \\ 0 \end{bmatrix}$
Therefore, $x= \dfrac{13}{16}; y=\dfrac{11}{16}; z= -2$
