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Simplifying 5(x + 2y) + 3(x + y) = 0 (x * 5 + 2y * 5) + 3(x + y) = 0 (5x + 10y) + 3(x + y) = 0 5x + 10y + (x * 3 + y * 3) = 0 5x + 10y + (3x + 3y) = 0 Reorder the terms: 5x + 3x + 10y + 3y = 0 Combine like terms: 5x + 3x = 8x 8x + 10y + 3y = 0 Combine like terms: 10y + 3y = 13y 8x + 13y = 0 Solving 8x + 13y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13y' to each side of the equation. 8x + 13y + -13y = 0 + -13y Combine like terms: 13y + -13y = 0 8x + 0 = 0 + -13y 8x = 0 + -13y Remove the zero: 8x = -13y Divide each side by '8'. x = -1.625y Simplifying x = -1.625y
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