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Simplifying 9(2x + 3y) + -6(4x + -2y) = 0 (2x * 9 + 3y * 9) + -6(4x + -2y) = 0 (18x + 27y) + -6(4x + -2y) = 0 18x + 27y + (4x * -6 + -2y * -6) = 0 18x + 27y + (-24x + 12y) = 0 Reorder the terms: 18x + -24x + 27y + 12y = 0 Combine like terms: 18x + -24x = -6x -6x + 27y + 12y = 0 Combine like terms: 27y + 12y = 39y -6x + 39y = 0 Solving -6x + 39y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-39y' to each side of the equation. -6x + 39y + -39y = 0 + -39y Combine like terms: 39y + -39y = 0 -6x + 0 = 0 + -39y -6x = 0 + -39y Remove the zero: -6x = -39y Divide each side by '-6'. x = 6.5y Simplifying x = 6.5y
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