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Solve for y. Assume the equation has a solution for y. {:[py+7=6y+q],[y=◻+=^(+)]:}

Solve for y y .\newlineAssume the equation has a solution for y y .\newlinepy+7=6y+qy=□ \begin{array}{l} p y+7=6 y+q \\ 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+7=6y+qy=□ \begin{array}{l} p y+7=6 y+q \\ y=\square \end{array}
  1. Identify the system: Identify the system of equations to solve for yy.\newlineThe system is:\newline11. py+7=6y+qp y + 7 = 6 y + q\newline22. y=?y = ?\newlineWe need to isolate yy in the first equation.
  2. Subtract py py from both sides: Subtract py py from both sides of the equation to move all terms containing y y to one side.\newline(py+7)−py=(6y+q)−py (py + 7) - py = (6y + q) - py \newlineThis simplifies to:\newline7=6y−py+q 7 = 6y - py + q
  3. Factor out y from the terms: Factor out y from the terms on the right-hand side.\newline77 = y(66 - p) + q\newlineNow we have y multiplied by (66 - p) and an additional q on the right-hand side.
  4. Subtract qq from both sides: Subtract qq from both sides to isolate the term with yy.\newline7−q=y(6−p)7 - q = y(6 - p)\newlineNow we have y(6−p)y(6 - p) on one side and 7−q7 - q on the other side.
  5. Divide both sides by (6−p)(6 - p): Divide both sides by (6−p)(6 - p) to solve for yy.7−q6−p=y\frac{7 - q}{6 - p} = yThis gives us the value of yy in terms of pp and qq.

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