Find all solutions to the system of equations:
$$abc^3=24$$ $$ab^3c=54$$ $$a^3bc=6$$
Well by guessing or trial and error, I was able to find
$a=1, b=3, c=2$
but it said find all solutions, so there is a possbility that there could be other solutions.
If $a=1, b=3, c=2$ is the only solutions, how would you solve the question more systematically instead of trial and error.