Nonlinear System (Part 2)

Algebra Level 4

$\large \begin {cases} abc = 2 \\ a^{2}b^{3}c^{4} = 5 \\ a^{-1}b^{7}c^{-2} = 9 \end {cases}$

If $a, b,$ and $c$ are real numbers, determine $(a + b + c)$ , to two decimal places.

Hint: Can you find a clever way of representing this as a linear system?