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Simplifying 5(2x + 3y) + -5(4x + -5y) = 0 (2x * 5 + 3y * 5) + -5(4x + -5y) = 0 (10x + 15y) + -5(4x + -5y) = 0 10x + 15y + (4x * -5 + -5y * -5) = 0 10x + 15y + (-20x + 25y) = 0 Reorder the terms: 10x + -20x + 15y + 25y = 0 Combine like terms: 10x + -20x = -10x -10x + 15y + 25y = 0 Combine like terms: 15y + 25y = 40y -10x + 40y = 0 Solving -10x + 40y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40y' to each side of the equation. -10x + 40y + -40y = 0 + -40y Combine like terms: 40y + -40y = 0 -10x + 0 = 0 + -40y -10x = 0 + -40y Remove the zero: -10x = -40y Divide each side by '-10'. x = 4y Simplifying x = 4y
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