Solve for y 6x+y=2y+8

$6 x + y = 2 y + 8$

Move all terms containing $y$ to the left side of the equation.

Subtract $2 y$ from both sides of the equation.

$6 x + y - 2 y = 8$

Subtract $2 y$ from $y$ .

$6 x - y = 8$

Subtract $6 x$ from both sides of the equation.

$- y = 8 - 6 x$

Divide each term in $- y = 8 - 6 x$ by $- 1$ and simplify.

Divide each term in $- y = 8 - 6 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{8}{- 1} + \frac{- 6 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{8}{- 1} + \frac{- 6 x}{- 1}$

Divide $y$ by $1$ .

$y = \frac{8}{- 1} + \frac{- 6 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $8$ by $- 1$ .

$y = - 8 + \frac{- 6 x}{- 1}$

Move the negative one from the denominator of $\frac{- 6 x}{- 1}$ .

$y = - 8 - 1 \cdot (- 6 x)$

Rewrite $- 1 \cdot (- 6 x)$ as $- (- 6 x)$ .

$y = - 8 - (- 6 x)$

Multiply $- 6$ by $- 1$ .

$y = - 8 + 6 x$