# For what temperature value are the celsius value and the Fahrenheit value the same?

##### 1 Answer

*For this, we will need to find an expression for the celsius scale and set it equal to the fahrenheit scale.*

Let **temperature** on the *fahrenheit* scale, and **temperature** on the *celsius* scale.

Recall that

The trick is to start by assuming that

If

#T_C = 9/5T_C + 32#

#5/5T_C = 9/5T_C + 32#

#-32 = 4/5T_C#

#color(blue)(T_C) = -32*5/4#

#= color(blue)(-40^@ "C")#

Now, let's test this claim by converting back to fahrenheit using the first equation we looked at.

#color(blue)(T_F) = 9/5*(-40^@ "C") + 32#

#= -72 + 32#

#= color(blue)(-40^@ "F")# #color(green)(sqrt"")#

Given that we were solving a linear equation, there exists one and only one solution. Thus, we have found all solutions.