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Simplifying 10x + 3x + y + 6z + -5x + 8y + -2z = 0 Reorder the terms: 10x + 3x + -5x + y + 8y + 6z + -2z = 0 Combine like terms: 10x + 3x = 13x 13x + -5x + y + 8y + 6z + -2z = 0 Combine like terms: 13x + -5x = 8x 8x + y + 8y + 6z + -2z = 0 Combine like terms: y + 8y = 9y 8x + 9y + 6z + -2z = 0 Combine like terms: 6z + -2z = 4z 8x + 9y + 4z = 0 Solving 8x + 9y + 4z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9y' to each side of the equation. 8x + 9y + -9y + 4z = 0 + -9y Combine like terms: 9y + -9y = 0 8x + 0 + 4z = 0 + -9y 8x + 4z = 0 + -9y Remove the zero: 8x + 4z = -9y Add '-4z' to each side of the equation. 8x + 4z + -4z = -9y + -4z Combine like terms: 4z + -4z = 0 8x + 0 = -9y + -4z 8x = -9y + -4z Divide each side by '8'. x = -1.125y + -0.5z Simplifying x = -1.125y + -0.5z
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