Every Equation Is Missing Something

Algebra Level 2

{x+y+u=4y+u+v=5u+v+x=0v+x+y=8 \large{\begin{cases} x + y + u = 4 \\ y + u + v = -5 \\ u + v +x = 0 \\ v + x + y = -8 \end{cases}}

Let x,y,ux,y,u and vv be numbers satisfying the system of equations above. Find the product xyuvxyuv.​

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