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Simplifying 2(4x + -9y) + 5(3y + -4x) = 0 (4x * 2 + -9y * 2) + 5(3y + -4x) = 0 (8x + -18y) + 5(3y + -4x) = 0 Reorder the terms: 8x + -18y + 5(-4x + 3y) = 0 8x + -18y + (-4x * 5 + 3y * 5) = 0 8x + -18y + (-20x + 15y) = 0 Reorder the terms: 8x + -20x + -18y + 15y = 0 Combine like terms: 8x + -20x = -12x -12x + -18y + 15y = 0 Combine like terms: -18y + 15y = -3y -12x + -3y = 0 Solving -12x + -3y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. -12x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 -12x + 0 = 0 + 3y -12x = 0 + 3y Remove the zero: -12x = 3y Divide each side by '-12'. x = -0.25y Simplifying x = -0.25y
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