The temperature at which the Fahrenheit and Celsius scales will give numerically equal (but opposite in sign) value

We are asked to find the temperatures in faherenheit & Celsius scale numerical equal but opposite in sign.

 Let the temperature$$\begin{gathered} =x^{0}C in celsius \\ Equivalent to =x^{0}F \\ We have relation \\ \frac{C}{100}=\frac{F-32}{180} \\ \Rightarrow \frac{x}{100}=\frac{-x-32}{180} \\ \Rightarrow \frac{x}{5}=\frac{-x-32}{9} \\ \Rightarrow 9x=-5x-160 \\ \therefore 14x=-160 \\ \therefore x=\frac{-160}{14}=-\frac{80}{7}=-11.{43}^{0}C \\ Then its -x^{0}F=11.{43}^{0}F \\ For -11.{43}^{0}C we get Fahrenheit measure 11.{43}^{0}F \\ Similarly if we consider \\ Temperature=x^{0}F \\ Then its equivalent in Celsius scale should be -x^{0}C \\ U\sin g relation \frac{C}{100}=\frac{F-32}{180} \\ \frac{-x}{100}=\frac{x-32}{180} \\ \Rightarrow \frac{-x}{5}=\frac{x-32}{9} \\ -9x=5x-160 \\ -14x=-160 \\ \therefore x=11.{43}^{0}F \\ Then its Celsius equivalent is -11.{43}^{0}F in both cases having same umerical value but opposite in sign. \end{gathered}$$