Solve the System of Equations C=5/9(F-32) F=9/5C+32

$C = \frac{5}{9} (F - 32)$ $F = \frac{9}{5} C + 32$

Step 1

Simplify $\frac{5}{9} \cdot (F - 32)$ .

Apply the distributive property.

$C = \frac{5}{9} F + \frac{5}{9} \cdot - 32$

$F = \frac{9}{5} C + 32$

Combine $\frac{5}{9}$ and $F$ .

$C = \frac{5 F}{9} + \frac{5}{9} \cdot - 32$

$F = \frac{9}{5} C + 32$

Multiply $\frac{5}{9} \cdot - 32$ .

Combine $\frac{5}{9}$ and $- 32$ .

$C = \frac{5 F}{9} + \frac{5 \cdot - 32}{9}$

$F = \frac{9}{5} C + 32$

Multiply $5$ by $- 32$ .

$C = \frac{5 F}{9} + \frac{- 160}{9}$

$F = \frac{9}{5} C + 32$

$C = \frac{5 F}{9} + \frac{- 160}{9}$

$F = \frac{9}{5} C + 32$

Move the negative in front of the fraction.

$C = \frac{5 F}{9} - \frac{160}{9}$

$F = \frac{9}{5} C + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

$F = \frac{9}{5} C + 32$

Step 2

Replace all occurrences of $C$ with $\frac{5 F}{9} - \frac{160}{9}$ in each equation.

Replace all occurrences of $C$ in $F = \frac{9}{5} C + 32$ with $\frac{5 F}{9} - \frac{160}{9}$ .

$F = \frac{9}{5} \cdot (\frac{5 F}{9} - \frac{160}{9}) + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

Simplify the right side.

Simplify $\frac{9}{5} \cdot (\frac{5 F}{9} - \frac{160}{9}) + 32$ .

Simplify each term.

Apply the distributive property.

$F = \frac{9}{5} \cdot \frac{5 F}{9} + \frac{9}{5} \cdot (- \frac{160}{9}) + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

Cancel the common factor of $9$ .

Cancel the common factor.

$F = \frac{9}{5} \cdot \frac{5 F}{9} + \frac{9}{5} \cdot (- \frac{160}{9}) + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

Rewrite the expression.

$F = \frac{1}{5} \cdot (5 F) + \frac{9}{5} \cdot (- \frac{160}{9}) + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

$F = \frac{1}{5} \cdot (5 F) + \frac{9}{5} \cdot (- \frac{160}{9}) + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

Cancel the common factor of $5$ .

Factor $5$ out of $5 F$ .

$F = \frac{1}{5} \cdot (5 (F)) + \frac{9}{5} \cdot (- \frac{160}{9}) + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

Cancel the common factor.

$F = \frac{1}{5} \cdot (5 F) + \frac{9}{5} \cdot (- \frac{160}{9}) + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

Rewrite the expression.

$F = F + \frac{9}{5} \cdot (- \frac{160}{9}) + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

$F = F + \frac{9}{5} \cdot (- \frac{160}{9}) + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{160}{9}$ into the numerator.

$F = F + \frac{9}{5} \cdot \frac{- 160}{9} + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

Cancel the common factor.

$F = F + \frac{9}{5} \cdot \frac{- 160}{9} + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

Rewrite the expression.

$F = F + \frac{1}{5} \cdot - 160 + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

$F = F + \frac{1}{5} \cdot - 160 + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

Cancel the common factor of $5$ .

Factor $5$ out of $- 160$ .

$F = F + \frac{1}{5} \cdot (5 (- 32)) + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

Cancel the common factor.

$F = F + \frac{1}{5} \cdot (5 \cdot - 32) + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

Rewrite the expression.

$F = F - 32 + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

$F = F - 32 + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

$F = F - 32 + 32$

$C = \frac{5 F}{9} - \frac{160}{9}$

Combine the opposite terms in $F - 32 + 32$ .

Add $- 32$ and $32$ .

$F = F + 0$

$C = \frac{5 F}{9} - \frac{160}{9}$

Add $F$ and $0$ .

$F = F$

$C = \frac{5 F}{9} - \frac{160}{9}$

$F = F$

$C = \frac{5 F}{9} - \frac{160}{9}$

$F = F$

$C = \frac{5 F}{9} - \frac{160}{9}$

$F = F$

$C = \frac{5 F}{9} - \frac{160}{9}$

$F = F$

$C = \frac{5 F}{9} - \frac{160}{9}$

Step 3

Remove any equations from the system that are always true.

$C = \frac{5 F}{9} - \frac{160}{9}$

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