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Simplifying 4.6(5x + -3y) + -5.2(8x + y) = 0 (5x * 4.6 + -3y * 4.6) + -5.2(8x + y) = 0 (23x + -13.8y) + -5.2(8x + y) = 0 23x + -13.8y + (8x * -5.2 + y * -5.2) = 0 23x + -13.8y + (-41.6x + -5.2y) = 0 Reorder the terms: 23x + -41.6x + -13.8y + -5.2y = 0 Combine like terms: 23x + -41.6x = -18.6x -18.6x + -13.8y + -5.2y = 0 Combine like terms: -13.8y + -5.2y = -19y -18.6x + -19y = 0 Solving -18.6x + -19y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19y' to each side of the equation. -18.6x + -19y + 19y = 0 + 19y Combine like terms: -19y + 19y = 0 -18.6x + 0 = 0 + 19y -18.6x = 0 + 19y Remove the zero: -18.6x = 19y Divide each side by '-18.6'. x = -1.021505376y Simplifying x = -1.021505376y
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