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Simplifying 6(2x + -3y) + -3(x + -4y) = 0 (2x * 6 + -3y * 6) + -3(x + -4y) = 0 (12x + -18y) + -3(x + -4y) = 0 12x + -18y + (x * -3 + -4y * -3) = 0 12x + -18y + (-3x + 12y) = 0 Reorder the terms: 12x + -3x + -18y + 12y = 0 Combine like terms: 12x + -3x = 9x 9x + -18y + 12y = 0 Combine like terms: -18y + 12y = -6y 9x + -6y = 0 Solving 9x + -6y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6y' to each side of the equation. 9x + -6y + 6y = 0 + 6y Combine like terms: -6y + 6y = 0 9x + 0 = 0 + 6y 9x = 0 + 6y Remove the zero: 9x = 6y Divide each side by '9'. x = 0.6666666667y Simplifying x = 0.6666666667y
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