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Simplifying (3x + -5y + z) + (5x + 6y + -4z) = 0 Remove parenthesis around (3x + -5y + z) 3x + -5y + z + (5x + 6y + -4z) = 0 Remove parenthesis around (5x + 6y + -4z) 3x + -5y + z + 5x + 6y + -4z = 0 Reorder the terms: 3x + 5x + -5y + 6y + z + -4z = 0 Combine like terms: 3x + 5x = 8x 8x + -5y + 6y + z + -4z = 0 Combine like terms: -5y + 6y = 1y 8x + 1y + z + -4z = 0 Combine like terms: z + -4z = -3z 8x + 1y + -3z = 0 Solving 8x + 1y + -3z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 8x + 1y + -1y + -3z = 0 + -1y Combine like terms: 1y + -1y = 0 8x + 0 + -3z = 0 + -1y 8x + -3z = 0 + -1y Remove the zero: 8x + -3z = -1y Add '3z' to each side of the equation. 8x + -3z + 3z = -1y + 3z Combine like terms: -3z + 3z = 0 8x + 0 = -1y + 3z 8x = -1y + 3z Divide each side by '8'. x = -0.125y + 0.375z Simplifying x = -0.125y + 0.375z
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