The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation `9C = 5F - 160^(@)`. If the temperature is `0^(@)` C, then what is the temperature in Fahrenheit and the temp is `0^(@)` F, then what is the temperature in Celsius ?

Options

A. `32^(@) F, 17. 78^(@)` C
B. `25^(@)` F, 16, `50^(@)`, C
C. `25^(@)` F, `-16,50^(@)`C
D. `32^(@)` F, `-17,78^(@)` C

Answer

To solve the problem, we will break it down into two parts based on the given linear equation that converts Fahrenheit (F) to Celsius (C):

\[ 9C = 5F - 160 \]

### Part 1: Finding Fahrenheit when Celsius is 0

1. **Set C to 0** in the equation:
\[ 9(0) = 5F - 160 \]
This simplifies to:
\[ 0 = 5F - 160 \]

2. **Rearrange the equation** to isolate \(F\):
\[ 5F = 160 \]

3. **Divide both sides by 5** to solve for \(F\):
\[ F = \frac{160}{5} = 32 \]

Thus, when the temperature is \(0^\circ C\), it is \(32^\circ F\).

### Part 2: Finding Celsius when Fahrenheit is 0

1. **Set F to 0** in the equation:
\[ 9C = 5(0) - 160 \]
This simplifies to:
\[ 9C = -160 \]

2. **Rearrange the equation** to isolate \(C\):
\[ C = \frac{-160}{9} \]

3. **Calculate the value**:
\[ C \approx -17.78 \]

Thus, when the temperature is \(0^\circ F\), it is approximately \(-17.78^\circ C\).

### Final Answers:
- When \(0^\circ C\), the temperature is \(32^\circ F\).
- When \(0^\circ F\), the temperature is approximately \(-17.78^\circ C\).