# How do you solve for y 9x + 3y - 5 = 6x - 9y + 10?

Oct 11, 2015

$\frac{5 - x}{4}$

#### Explanation:

Your goal here is to isolate $y$ on one side of the equation.

This implies that you need to have all the $x$-terms and all the integers on the other side of the equation. Your starting equation looks like this

$9 x + 3 y - 5 = 6 x - 9 y + 10$

Start by adding $5$ to both sides of the equation

$9 x + 3 y - \textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} = 6 x - 9 y + 10 + 5$

$9 x + 3 y = 6 x - 9 y + 15$

Next, add $9 y$ to both sides of the equation

$9 x + 3 y + 9 y = 6 x - \textcolor{red}{\cancel{\textcolor{b l a c k}{9 y}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{9 y}}} + 15$

$9 x + 12 y = 6 x + 15$

Next, add $- 9 x$ to both sides

$\textcolor{red}{\cancel{\textcolor{b l a c k}{9 x}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{9 x}}} + 12 y = 6 x - 9 x + 15$

$12 y = - 3 x + 15$

Finally, divide both sides by $12$ and simplify where possible

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{12}}} y}{\textcolor{red}{\cancel{\textcolor{b l a c k}{12}}}} = \frac{- 3 x + 15}{12}$

$y = \textcolor{g r e e n}{\frac{5 - x}{4}}$