4・143 Solve the system of equations
$$\left\{\begin{array}{l}
x-y+z=1, \\
y-z+u=2, \\
z-u+v=3, \\
u-v+x=4, \\
v-x+y=5
\end{array}\right.$$
[Solution] (2) $+(3)-(5)$ gives $x=0$,
(3) + (4) - (1) gives
$y=6$,
(4) + (5) - (2) gives
$z=7$
(5) + (1) - (3) gives
$u=3$,
(1) + (2) - (4) gives
$v=-1$.
Upon verification, the solution to the original system of equations is
$$\left\{\begin{array}{l}
x=0 \\
y=6 \\
z=7 \\
u=3 \\
v=-1
\end{array}\right.$$