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Simplifying 5(x + 2y) + -1(2x + 5y) = 0 (x * 5 + 2y * 5) + -1(2x + 5y) = 0 (5x + 10y) + -1(2x + 5y) = 0 5x + 10y + (2x * -1 + 5y * -1) = 0 5x + 10y + (-2x + -5y) = 0 Reorder the terms: 5x + -2x + 10y + -5y = 0 Combine like terms: 5x + -2x = 3x 3x + 10y + -5y = 0 Combine like terms: 10y + -5y = 5y 3x + 5y = 0 Solving 3x + 5y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 3x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 3x + 0 = 0 + -5y 3x = 0 + -5y Remove the zero: 3x = -5y Divide each side by '3'. x = -1.666666667y Simplifying x = -1.666666667y
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