# Question #191af

Sep 6, 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

First, subtract $\textcolor{red}{3 x}$ from each side of the equation to place both the $x$ and $y$ variables on the left side of the equation while keeping the equation balanced:

$- \textcolor{red}{3 x} + y = - \textcolor{red}{3 x} + 3 x + 5$

$- 3 x + y = 0 + 5$

$- 3 x + y = 5$

Now, multiply each side of the equation by $\textcolor{red}{- 1}$ to make the $x$ coefficient a positive integer while keeping the equation balanced:

$\textcolor{red}{- 1} \left(- 3 x + y\right) = \textcolor{red}{- 1} \times 5$

$\left(\textcolor{red}{- 1} \times - 3 x\right) + \left(\textcolor{red}{- 1} \times y\right) = - 5$

$3 x + \left(- 1 y\right) = - 5$

$\textcolor{red}{3} x - \textcolor{b l u e}{1} y = \textcolor{g r e e n}{- 5}$