Answer
See graph below.
Yes, $F=C=-40^{\circ}$
Work Step by Step
See attached image (graphed with desmos.com).
We want find the intersection of the two lines.
Substitute $C=F $ into the given equation:
$F=\displaystyle \frac{5}{9}(F-32)\qquad/\times 9$
$9F=5(F-32)$
$9F=5F-160$
$4F=-160$
$F=-40^{\circ}\qquad (C=-40^{\circ})$
