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Simplifying 69(6x + -9y) + 6(9x + -69y) = 0 (6x * 69 + -9y * 69) + 6(9x + -69y) = 0 (414x + -621y) + 6(9x + -69y) = 0 414x + -621y + (9x * 6 + -69y * 6) = 0 414x + -621y + (54x + -414y) = 0 Reorder the terms: 414x + 54x + -621y + -414y = 0 Combine like terms: 414x + 54x = 468x 468x + -621y + -414y = 0 Combine like terms: -621y + -414y = -1035y 468x + -1035y = 0 Solving 468x + -1035y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1035y' to each side of the equation. 468x + -1035y + 1035y = 0 + 1035y Combine like terms: -1035y + 1035y = 0 468x + 0 = 0 + 1035y 468x = 0 + 1035y Remove the zero: 468x = 1035y Divide each side by '468'. x = 2.211538462y Simplifying x = 2.211538462y
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