+1859 The real numbers $p$, $q$, $r$, $x$, $y$, and $z$ satisfy
\begin{align*}
px+qy+rz&=7,\\
p+qx+ry&=z+5,\\
pz+q+rx&=y-3,\\
py+qz+r&=x+4,\\
p+q+r&=-8.
\end{align*}
Find $x+y+z$.
+129771 Add the equations
p(x + y + z) + 2p + q(x + y + z) + 2q + r(x + y + z) + 2r = (x + y + z) + 7 + 5 - 3 + 4 - 8
(p + q + r) ( x + y + z) + 2 (p + q + r) = (x + y + z) + 5
(-8) (x + y + z) + 2 (-8) = (x + y + z) + 5
-9 (x + y + z) = 5 - 2(-8)
-9 (x + y + z) = 5 + 16
-9 (x + y + z) = 21
(x + y + z) = -21 / 9 = -7/ 3
