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Simplifying x + x + -1x + y + y + y + -1z + z + -1z = 0 Combine like terms: x + x = 2x 2x + -1x + y + y + y + -1z + z + -1z = 0 Combine like terms: 2x + -1x = 1x 1x + y + y + y + -1z + z + -1z = 0 Combine like terms: y + y = 2y 1x + 2y + y + -1z + z + -1z = 0 Combine like terms: 2y + y = 3y 1x + 3y + -1z + z + -1z = 0 Combine like terms: -1z + z = 0 1x + 3y + 0 + -1z = 0 1x + 3y + -1z = 0 Solving 1x + 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. 1x + 3y + -3y + -1z = 0 + -3y Combine like terms: 3y + -3y = 0 1x + 0 + -1z = 0 + -3y 1x + -1z = 0 + -3y Remove the zero: 1x + -1z = -3y Add 'z' to each side of the equation. 1x + -1z + z = -3y + z Combine like terms: -1z + z = 0 1x + 0 = -3y + z 1x = -3y + z Divide each side by '1'. x = -3y + z Simplifying x = -3y + z
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