To solve the equation for [tex]\( y \)[/tex] given by:
[tex]\[ p y + q y = -4 y + 8, \][/tex]
we can follow these steps:
1. Combine like terms on both sides of the equation.
On the left-hand side, combine [tex]\( p y \)[/tex] and [tex]\( q y \)[/tex]:
[tex]\[ (p + q) y = -4 y + 8. \][/tex]
2. Move all terms involving [tex]\( y \)[/tex] to one side of the equation. Add [tex]\( 4y \)[/tex] to both sides to accomplish this:
[tex]\[ (p + q) y + 4 y = 8. \][/tex]
3. Factor out [tex]\( y \)[/tex] on the left-hand side:
[tex]\[ (p + q + 4) y = 8. \][/tex]
4. Solve for [tex]\( y \)[/tex] by dividing both sides of the equation by [tex]\( (p + q + 4) \)[/tex]:
[tex]\[ y = \frac{8}{p + q + 4}. \][/tex]
Hence, the solution for [tex]\( y \)[/tex] is:
[tex]\[ y = \frac{8}{p + q + 4}. \][/tex]
