10.1. One degree on the Celsius scale is equal to 1.8 degrees on the Fahrenheit scale, while $0^{\circ}$ Celsius corresponds to $32^{\circ}$ Fahrenheit. Can a temperature be expressed by the same number of degrees on both the Celsius and Fahrenheit scales?
Answer: Yes, it can.

From the condition, it follows that the temperature in Fahrenheit is expressed through the temperature in Celsius as follows: $T_{F}=1.8 T_{C}+32^{\circ}$. If $T_{F}=T_{C}$, then $0.8 T_{C}+32=0$, that is, $T_{C}=-40$.

Remarks. An answer without explanations - 0 points; an answer with explanations (it is not necessary to find the root of the equation - it is enough to note that the graphs of linear functions with unequal slopes intersect) - 7 points.