# How do you solve for y given 2x+3y-11=0?

Jan 8, 2017

See the full explanation below

#### Explanation:

Step 1) Add and subtract the necessary terms from each side of the equation to isolate the $y$ term while keeping the equation balanced:

$2 x + 3 y - 11 - \textcolor{red}{2 x} + \textcolor{b l u e}{11} = 0 - \textcolor{red}{2 x} + \textcolor{b l u e}{11}$

$2 x - \textcolor{red}{2 x} + 3 y - 11 + \textcolor{b l u e}{11} = 0 - \textcolor{red}{2 x} + \textcolor{b l u e}{11}$

$0 + 3 y - 0 = - 2 x + 11$

$3 y = - 2 x + 11$

Step 2) Divide each side of the equation by $\textcolor{red}{3}$ to solve for $y$ while keeping the equation balanced:

$\frac{3 y}{\textcolor{red}{3}} = \frac{- 2 x + 11}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} y}{\cancel{\textcolor{red}{3}}} = - \frac{2}{\textcolor{red}{3}} x + \frac{11}{\textcolor{red}{3}}$

$y = - \frac{2}{3} x + \frac{11}{3}$