In the solution to this system, what is the value of c?

$\displaystyle{5}{a}+{4}{b}=-{6}\usepackage{cmbright}\Huge\$

$\displaystyle-{2}{a}+{c}={2}\usepackage{cmbright}\Huge\$

$\displaystyle-{6}{b}-{5}{c}=-{6}\usepackage{cmbright}\Huge\$

$\displaystyle{c}=\usepackage{cmbright}\Huge\$ _____