At what temperature do the Fahrenheit and Celsius scales give the same reading? 

For a temperature in Fahrenheit T_F and a temperature in Celsius T_C,

The relation given is 
$T_F= \frac{9}{5}{T}_C+ 32$ 

Let,  $T_F= T_C$

then,

$T_C= \frac{9}{5}{T}_C+ 32$

$\frac{-4}{5}{T}_C= 32$

$T_C= -{40}^0$ ($T_F= T_C$)

Therefore, the Fahrenheit and the Celsius scale give the same reading at - 40^o.