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

$\displaystyle{5}{d}+{3}{e}+{2}{f{=}}{8}\usepackage{cmbright}\Huge\$

$\displaystyle-{3}{d}+{2}{e}-{2}{f{=}}{8}\usepackage{cmbright}\Huge\$

$\displaystyle-{7}{d}+{e}-{2}{f{=}}{12}\usepackage{cmbright}\Huge\$

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