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Simplifying 5(x + -2y) + 3(x + -1y) + -1(3x + -3y) = 0 (x * 5 + -2y * 5) + 3(x + -1y) + -1(3x + -3y) = 0 (5x + -10y) + 3(x + -1y) + -1(3x + -3y) = 0 5x + -10y + (x * 3 + -1y * 3) + -1(3x + -3y) = 0 5x + -10y + (3x + -3y) + -1(3x + -3y) = 0 5x + -10y + 3x + -3y + (3x * -1 + -3y * -1) = 0 5x + -10y + 3x + -3y + (-3x + 3y) = 0 Reorder the terms: 5x + 3x + -3x + -10y + -3y + 3y = 0 Combine like terms: 5x + 3x = 8x 8x + -3x + -10y + -3y + 3y = 0 Combine like terms: 8x + -3x = 5x 5x + -10y + -3y + 3y = 0 Combine like terms: -10y + -3y = -13y 5x + -13y + 3y = 0 Combine like terms: -13y + 3y = -10y 5x + -10y = 0 Solving 5x + -10y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10y' to each side of the equation. 5x + -10y + 10y = 0 + 10y Combine like terms: -10y + 10y = 0 5x + 0 = 0 + 10y 5x = 0 + 10y Remove the zero: 5x = 10y Divide each side by '5'. x = 2y Simplifying x = 2y
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