# How do you solve: 5y - 2 = 2y + 19?

Jan 14, 2017

See full solution process below:

#### Explanation:

First we need to add and subtract the necessary terms from each side of the equation to isolate the $y$ terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:

$5 y - 2 - \textcolor{red}{2 y} + \textcolor{b l u e}{2} = 2 y + 19 - \textcolor{red}{2 y} + \textcolor{b l u e}{2}$

$5 y - \textcolor{red}{2 y} - 2 + \textcolor{b l u e}{2} = 2 y - \textcolor{red}{2 y} + 19 + \textcolor{b l u e}{2}$

$\left(5 - 2\right) y - 0 = 0 + 21$

$3 y = 21$

We can now divide each side of the equation by $\textcolor{red}{3}$ to solve for $y$ while keeping the equation balanced:

$\frac{3 y}{\textcolor{red}{3}} = \frac{21}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} y}{\cancel{\textcolor{red}{3}}} = 7$

$y = 7$