1. For what values of $a, b$, and $c$ do the lines $y=a x+b, y=b x+c, y=c x+a$ pass through the point $(1 ; 3)$?
# Solution.

The lines $y=a x+b, y=b x+c, y=c x+a$ pass through the point $(1 ; 3)$ if and only if $a, b$ and $c$ satisfy the system of equations:

$$
\left\{\begin{array}{l}
3=a+b \\
3=b+c \\
3=c+a
\end{array}\right.
$$

By adding the equations, we get: $9=2(a+b+c) \Rightarrow a+b+c=4.5$. Subtracting the first, second, and third equations from the last equality in turn, we obtain: $a=b=c=1.5$.

Answer: $a=b=c=1.5$.

Instructions. Only the answer - 0 points; the system of equations written - 1 point.