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Simplifying 0 = 8(x + y + Z) + -6(x + y + -1z) Reorder the terms: 0 = 8(Z + x + y) + -6(x + y + -1z) 0 = (Z * 8 + x * 8 + y * 8) + -6(x + y + -1z) 0 = (8Z + 8x + 8y) + -6(x + y + -1z) 0 = 8Z + 8x + 8y + (x * -6 + y * -6 + -1z * -6) 0 = 8Z + 8x + 8y + (-6x + -6y + 6z) Reorder the terms: 0 = 8Z + 8x + -6x + 8y + -6y + 6z Combine like terms: 8x + -6x = 2x 0 = 8Z + 2x + 8y + -6y + 6z Combine like terms: 8y + -6y = 2y 0 = 8Z + 2x + 2y + 6z Solving 0 = 8Z + 2x + 2y + 6z Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-8Z' to each side of the equation. 0 + -8Z = 8Z + 2x + 2y + -8Z + 6z Remove the zero: -8Z = 8Z + 2x + 2y + -8Z + 6z Reorder the terms: -8Z = 8Z + -8Z + 2x + 2y + 6z Combine like terms: 8Z + -8Z = 0 -8Z = 0 + 2x + 2y + 6z -8Z = 2x + 2y + 6z Divide each side by '-8'. Z = -0.25x + -0.25y + -0.75z Simplifying Z = -0.25x + -0.25y + -0.75z
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