Solve for y py+qy=-4y+8

$p y + q y = - 4 y + 8$

Add $4 y$ to both sides of the equation.

$p y + q y + 4 y = 8$

Factor $y$ out of $p y + q y + 4 y$ .

Factor $y$ out of $p y$ .

$y p + q y + 4 y = 8$

Factor $y$ out of $q y$ .

$y p + y q + 4 y = 8$

Factor $y$ out of $4 y$ .

$y p + y q + y \cdot 4 = 8$

Factor $y$ out of $y p + y q$ .

$y (p + q) + y \cdot 4 = 8$

Factor $y$ out of $y (p + q) + y \cdot 4$ .

$y (p + q + 4) = 8$

Divide each term in $y (p + q + 4) = 8$ by $p + q + 4$ and simplify.

Divide each term in $y (p + q + 4) = 8$ by $p + q + 4$ .

$\frac{y (p + q + 4)}{p + q + 4} = \frac{8}{p + q + 4}$

Simplify the left side.

Cancel the common factor of $p + q + 4$ .

Cancel the common factor.

$\frac{y (p + q + 4)}{p + q + 4} = \frac{8}{p + q + 4}$

Divide $y$ by $1$ .

$y = \frac{8}{p + q + 4}$