Must be Algebra

Algebra Level 4

$\begin{cases} x + 7y + 3v + 5u = 16 \\ 8x + 4y + 6v + 2u = -16 \\ 2x + 6y + 4v + 8u = 16 \\ 5x + 3y + 7v + u = -16 \end{cases}$

Real numbers $x$ , $y$ , $u$ , and $v$ satisfy the system of equations above. Find $xyuv$ .