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Simplifying 4(2x + -2y) + 5(2y + -1x) = 0 (2x * 4 + -2y * 4) + 5(2y + -1x) = 0 (8x + -8y) + 5(2y + -1x) = 0 Reorder the terms: 8x + -8y + 5(-1x + 2y) = 0 8x + -8y + (-1x * 5 + 2y * 5) = 0 8x + -8y + (-5x + 10y) = 0 Reorder the terms: 8x + -5x + -8y + 10y = 0 Combine like terms: 8x + -5x = 3x 3x + -8y + 10y = 0 Combine like terms: -8y + 10y = 2y 3x + 2y = 0 Solving 3x + 2y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 3x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 3x + 0 = 0 + -2y 3x = 0 + -2y Remove the zero: 3x = -2y Divide each side by '3'. x = -0.6666666667y Simplifying x = -0.6666666667y
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