# How do you write 1/3x-1/3y=-2 in standard form and what is A, B, C?

Feb 7, 2017

$\textcolor{red}{1} x - \textcolor{b l u e}{1} y = \textcolor{g r e e n}{- 6}$

#### Explanation:

The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

To transform this equation into standard form we need to multiply each side of the equation by $\textcolor{red}{3}$ which will also keep the equation balanced:

$\textcolor{red}{3} \left(\frac{1}{3} x - \frac{1}{3} y\right) = \textcolor{red}{3} \times - 2$

(color(red)(3) xx 1/3x) - color(red)(3) xx 1/3y) = -6

$\frac{3}{3} x - \frac{3}{3} y = - 6$

$1 x - 1 y = - 6$