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Simplifying (x + 2y + -4z) + -1(x + -3y + 5z) = 0 Remove parenthesis around (x + 2y + -4z) x + 2y + -4z + -1(x + -3y + 5z) = 0 x + 2y + -4z + (x * -1 + -3y * -1 + 5z * -1) = 0 x + 2y + -4z + (-1x + 3y + -5z) = 0 Reorder the terms: x + -1x + 2y + 3y + -4z + -5z = 0 Combine like terms: x + -1x = 0 0 + 2y + 3y + -4z + -5z = 0 2y + 3y + -4z + -5z = 0 Combine like terms: 2y + 3y = 5y 5y + -4z + -5z = 0 Combine like terms: -4z + -5z = -9z 5y + -9z = 0 Solving 5y + -9z = 0 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9z' to each side of the equation. 5y + -9z + 9z = 0 + 9z Combine like terms: -9z + 9z = 0 5y + 0 = 0 + 9z 5y = 0 + 9z Remove the zero: 5y = 9z Divide each side by '5'. y = 1.8z Simplifying y = 1.8z
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