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Solve for y. Assume the equation has a solution for y. {:[py+qy=-4y+8],[y=◻]:}

Solve for y y .\newlineAssume the equation has a solution for y y .\newlinepy+qy=−4y+8y=□ \begin{array}{l} p y+q y=-4 y+8 \\ y=\square \end{array}

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Full solution

Q. Solve for y y .\newlineAssume the equation has a solution for y y .\newlinepy+qy=−4y+8y=□ \begin{array}{l} p y+q y=-4 y+8 \\ y=\square \end{array}
  1. Combine like terms: Combine like terms on the left side of the equation. py+qy=−4y+8py + qy = -4y + 8 can be rewritten as (p+q)y=−4y+8(p + q)y = -4y + 8.
  2. Add yy terms: Add 4y4y to both sides to get all the yy terms on one side.\newline(p+q)y+4y=−4y+8+4y(p + q)y + 4y = -4y + 8 + 4y simplifies to (p+q+4)y=8(p + q + 4)y = 8.
  3. Factor out y: Factor out y on the left side.\newliney(p + q + 44) = 88.
  4. Divide to solve for y: Divide both sides by (p+q+4)(p + q + 4) to solve for y.\newliney=8(p+q+4)y = \frac{8}{(p + q + 4)}.

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