How do you write 2x - 4y - 14 = 0 in standard form?

Jan 22, 2017

$\textcolor{red}{1} x - \textcolor{b l u e}{2} y = \textcolor{g r e e n}{7}$

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

We can first add $\textcolor{red}{14}$ to each side of the equation to have the constant on the right side of the equation while keeping the equation balanced:

$2 x - 4 y - 14 + \textcolor{red}{14} = 0 + \textcolor{red}{14}$

$2 x - 4 y - 0 = 14$

$2 x - 4 y = 14$

We can now divide each side of the equation by $\textcolor{red}{2}$ to eliminate a common factor of each term while keeping the equation balanced:

$\frac{2 x - 4 y}{\textcolor{red}{2}} = \frac{14}{\textcolor{red}{2}}$

$\frac{2 x}{\textcolor{red}{2}} - \frac{4 y}{\textcolor{red}{2}} = 7$

$x - 2 y = 7$

$\textcolor{red}{1} x - \textcolor{b l u e}{2} y = \textcolor{g r e e n}{7}$