# How do you solve for y in 3x + y = -6?

May 4, 2016

$y = - 3 x - 6$

#### Explanation:

The objective is to have just one $y$ and for it to be on one side of = and everything else on the other side.

Given:$\text{ } \textcolor{b r o w n}{3 x + y = - 6}$

Subtract $\textcolor{b l u e}{3 x}$ from both sides

$\textcolor{b r o w n}{3 x \textcolor{b l u e}{- 3 x} + y = - 6 \textcolor{b l u e}{- 3 x}}$

But $3 x - 3 x = 0$

$0 + y = - 3 x = 6$

$y = - 3 x - 6$

May 4, 2016

y = -6 - 3x

#### Explanation:

We want the y term to stay where it is on the left side and all other terms to be on the right side.

To achieve this subtract 3x from both sides.

$\Rightarrow \cancel{3 x} + y - \cancel{3 x} = - 6 - 3 x$

$\Rightarrow y = - 6 - 3 x$