solve system equation: $ a \cdot b = 3 \cdot a-b+1, b \cdot c = 3 \cdot b - c + 1, c \cdot a = 3 \cdot c - a + 1$

Question

I want to solve this system of equations but i'm stuck. Here is it:

$$ a \cdot b = 3 \cdot a - b + 1 $$ $$ b \cdot c = 3 \cdot b - c + 1 $$ $$ c \cdot a = 3 \cdot c - a + 1 $$

Answer 1

Hint: If $a\neq-1\wedge b\neq-1\wedge c\neq -1$

$$\begin{cases}b=\frac{3a+1}{1+a}\\c=\frac{3b+1}{1+b}\\a=\frac{3c+1}{1+c}\end{cases}$$

What happens if you substitute (1) in (2) and, after that, (2) in (3)?