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Simplifying 3x + 5y + -1z = 0 Solving 3x + 5y + -1z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 3x + 5y + -5y + -1z = 0 + -5y Combine like terms: 5y + -5y = 0 3x + 0 + -1z = 0 + -5y 3x + -1z = 0 + -5y Remove the zero: 3x + -1z = -5y Add 'z' to each side of the equation. 3x + -1z + z = -5y + z Combine like terms: -1z + z = 0 3x + 0 = -5y + z 3x = -5y + z Divide each side by '3'. x = -1.666666667y + 0.3333333333z Simplifying x = -1.666666667y + 0.3333333333z
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