# How do you write -3y - 6x = 10 in standard form?

Jul 19, 2017

See a solution process below:

#### 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

Step 1) Switch the $x$ and $y$ terms on the left side of the equation to meet the requirements of the Standard Formula:

$- 3 y - 6 x = 10$

$- 6 x - 3 y = 10$

Step 2)Multiply each side of the equation by $\textcolor{red}{- 1}$ to make the coefficient of the $x$ term non-negative as required by the formula while keeping the equation balanced:

$\textcolor{red}{- 1} \left(- 6 x - 3 y\right) = \textcolor{red}{- 1} \times 10$

$\left(\textcolor{red}{- 1} \times - 6 x\right) + \left(\textcolor{red}{- 1} \times - 3 y\right) = - 10$

$\textcolor{red}{6} x + \textcolor{b l u e}{3} y = \textcolor{g r e e n}{- 10}$