1. (40 points) Find the real solutions for the system of equations in $w, x, y, z$:
$$
\left\{\begin{array}{l}
w+8 x+3 y+5 z=20 \\
4 w+7 x+2 y+3 z=-20 \\
6 w+3 x+8 y+7 z=20 \\
7 w+2 x+7 y+3 z=-20 .
\end{array}\right.
$$
(1) + (4) gives $8(w+z)+10(x+y)=0$.
(2) + (3) gives $10(w+z)+10(x+y)=0$.

Thus, $w+z=0$ and $x+y=0$.
Substituting $y=-x$ and $z=-w$ into equations (1) and (2) yields $5 x-4 w=20, w+5 x=-20$.
Eliminating $x$ gives $-5 w=40$, i.e., $w=-8$.
From this, we get $x=-\frac{12}{5}, y=\frac{12}{5}, z=8$.