1. Stating the problem: We are given the equation $$3(3y - 4x) + 4(5x - 6) = 2(4y - 9) - 13$$ and need to transform it into normal form and solve for the unknown $y$. 2. Expand both sides: $$3(3y - 4x) = 9y - 12x$$ $$4(5x - 6) = 20x - 24$$ $$2(4y - 9) = 8y - 18$$ So the equation becomes: $$9y - 12x + 20x - 24 = 8y - 18 - 13$$ 3. Simplify both sides: Left side: $$9y + ( -12x + 20x ) - 24 = 9y + 8x - 24$$ Right side: $$8y - 31$$ So: $$9y + 8x - 24 = 8y - 31$$ 4. Bring all terms involving $y$ to one side and constants to the other: $$9y - 8y = -31 + 24 - 8x$$ $$y = -7 - 8x$$ This is the normal form with $y$ expressed in terms of $x$. 5. Next, find the value of $x$ from the equation $$4x + 0.5y = 2$$ when $$y = -4$$. Substitute $y = -4$: $$4x + 0.5(-4) = 2$$ $$4x - 2 = 2$$ 6. Solve for $x$: $$4x = 4$$ $$x = 1$$ Final answers: - Normal form: $$y = -7 - 8x$$ - When $$y = -4$$, $$x = 1$$