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Simplifying 6x + 3y + -1z = 0 Solving 6x + 3y + -1z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 6x + 3y + -3y + -1z = 0 + -3y Combine like terms: 3y + -3y = 0 6x + 0 + -1z = 0 + -3y 6x + -1z = 0 + -3y Remove the zero: 6x + -1z = -3y Add 'z' to each side of the equation. 6x + -1z + z = -3y + z Combine like terms: -1z + z = 0 6x + 0 = -3y + z 6x = -3y + z Divide each side by '6'. x = -0.5y + 0.1666666667z Simplifying x = -0.5y + 0.1666666667z
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