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Simplifying (2x + -1y + 4z) + -1(2x + -8z + y) = 0 Remove parenthesis around (2x + -1y + 4z) 2x + -1y + 4z + -1(2x + -8z + y) = 0 Reorder the terms: 2x + -1y + 4z + -1(2x + y + -8z) = 0 2x + -1y + 4z + (2x * -1 + y * -1 + -8z * -1) = 0 2x + -1y + 4z + (-2x + -1y + 8z) = 0 Reorder the terms: 2x + -2x + -1y + -1y + 4z + 8z = 0 Combine like terms: 2x + -2x = 0 0 + -1y + -1y + 4z + 8z = 0 -1y + -1y + 4z + 8z = 0 Combine like terms: -1y + -1y = -2y -2y + 4z + 8z = 0 Combine like terms: 4z + 8z = 12z -2y + 12z = 0 Solving -2y + 12z = 0 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-12z' to each side of the equation. -2y + 12z + -12z = 0 + -12z Combine like terms: 12z + -12z = 0 -2y + 0 = 0 + -12z -2y = 0 + -12z Remove the zero: -2y = -12z Divide each side by '-2'. y = 6z Simplifying y = 6z
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