# Unsolved ChallengeSystem of Equations

#### anemone

##### MHB POTW Director
Staff member
Find all the real numbers $a,\,b$ and $c$ that satisfy the following system of equations:

\begin{align*}a + b + c &= 1\\ \dfrac{a}{ 1 - a}+\dfrac{b}{1 - b} + \dfrac{c}{1 - c} &= 6ac + 6bc = (a + 1)(b + 1)\end{align*}

MHB Math Helper
Ick!

-Dan