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Simplifying (x + 3y + -5z) + -1(x + -2y + 6z) = 0 Remove parenthesis around (x + 3y + -5z) x + 3y + -5z + -1(x + -2y + 6z) = 0 x + 3y + -5z + (x * -1 + -2y * -1 + 6z * -1) = 0 x + 3y + -5z + (-1x + 2y + -6z) = 0 Reorder the terms: x + -1x + 3y + 2y + -5z + -6z = 0 Combine like terms: x + -1x = 0 0 + 3y + 2y + -5z + -6z = 0 3y + 2y + -5z + -6z = 0 Combine like terms: 3y + 2y = 5y 5y + -5z + -6z = 0 Combine like terms: -5z + -6z = -11z 5y + -11z = 0 Solving 5y + -11z = 0 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11z' to each side of the equation. 5y + -11z + 11z = 0 + 11z Combine like terms: -11z + 11z = 0 5y + 0 = 0 + 11z 5y = 0 + 11z Remove the zero: 5y = 11z Divide each side by '5'. y = 2.2z Simplifying y = 2.2z
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