Solve the following system of equations:

$$
\begin{gathered}
a x+b y-c z=2 a b \\
a x-b y+c z=2 a c \\
-a x+b y-c z=2 b c
\end{gathered}
$$
By adding the first and second equations:

$$
2 a x=2 a b+2 a c
$$

or

$$
x=b+c \text {. }
$$

Similarly, by adding the first and third, as well as the second and third equations, we obtain

$$
y=a+c \text { and } z=a+b \text {. }
$$

(Ferenc Szirtes, Pécs.)

Number of solutions: 28.