1. Stating the problem: Solve the system of equations by eliminating $x$ first: $$4x - 4y = 4$$ $$5x - 3y = 18$$ 2. Multiply the first equation by 5 and the second equation by 4 to align the coefficients of $x$: $$5(4x - 4y) = 5(4) \implies 20x - 20y = 20$$ $$4(5x - 3y) = 4(18) \implies 20x - 12y = 72$$ 3. Subtract the second new equation from the first to eliminate $x$: $$(20x - 20y) - (20x - 12y) = 20 - 72$$ $$20x - 20y - 20x + 12y = -52$$ $$-8y = -52$$ 4. Solve for $y$: $$y = \frac{-52}{-8} = \frac{52}{8} = \frac{13}{2} = 6.5$$ 5. Substitute $y=6.5$ into the first original equation to find $x$: $$4x - 4(6.5) = 4$$ $$4x - 26 = 4$$ $$4x = 30$$ $$x = \frac{30}{4} = 7.5$$ Final answer: $$x=7.5,\ y=6.5$$