1 makes everything beautiful

Let x,y,zx,y,z be integers such that

xy+x+y=20zy+z+y=6xz+x+z=2xy+x+y=20\\ zy+z+y=6\\ xz+x+z=2

Given that x,y,z0x,y,z\neq 0, find zxyz-x-y

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