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