# How do you write 1/2x+1/2y=6 in standard form and what is A, B, C?

Aug 2, 2017

$1 x + 1 y = 12$

#### Explanation:

"standard form" for a linear equation is
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{m a \ge n t a}{C}$
where
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{A} , \textcolor{b l u e}{B} , \textcolor{m a \ge n t a}{C}$ are integers
$\textcolor{w h i t e}{\text{XXX}}$(and usually with the restriction that $\textcolor{red}{A} \ge 0$)

Given
$\textcolor{w h i t e}{\text{XXX}} \frac{1}{2} x + \frac{1}{2} y = 6$
Multiplying everything by $2$ converts the coefficients to integers:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{1} x + \textcolor{b l u e}{1} y = \textcolor{m a \ge n t a}{12}$

Relating this back to the "standard form" we have
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{A} = \textcolor{red}{1}$
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{B} = \textcolor{b l u e}{1}$ and
$\textcolor{w h i t e}{\text{XXX}} \textcolor{m a \ge n t a}{C} = \textcolor{m a \ge n t a}{12}$