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Simplifying -3(y + -2z) + 5(2y + -1z) + 3(y + -3z) + -2(-4y + 2z) = 0 (y * -3 + -2z * -3) + 5(2y + -1z) + 3(y + -3z) + -2(-4y + 2z) = 0 (-3y + 6z) + 5(2y + -1z) + 3(y + -3z) + -2(-4y + 2z) = 0 -3y + 6z + (2y * 5 + -1z * 5) + 3(y + -3z) + -2(-4y + 2z) = 0 -3y + 6z + (10y + -5z) + 3(y + -3z) + -2(-4y + 2z) = 0 -3y + 6z + 10y + -5z + (y * 3 + -3z * 3) + -2(-4y + 2z) = 0 -3y + 6z + 10y + -5z + (3y + -9z) + -2(-4y + 2z) = 0 -3y + 6z + 10y + -5z + 3y + -9z + (-4y * -2 + 2z * -2) = 0 -3y + 6z + 10y + -5z + 3y + -9z + (8y + -4z) = 0 Reorder the terms: -3y + 10y + 3y + 8y + 6z + -5z + -9z + -4z = 0 Combine like terms: -3y + 10y = 7y 7y + 3y + 8y + 6z + -5z + -9z + -4z = 0 Combine like terms: 7y + 3y = 10y 10y + 8y + 6z + -5z + -9z + -4z = 0 Combine like terms: 10y + 8y = 18y 18y + 6z + -5z + -9z + -4z = 0 Combine like terms: 6z + -5z = 1z 18y + 1z + -9z + -4z = 0 Combine like terms: 1z + -9z = -8z 18y + -8z + -4z = 0 Combine like terms: -8z + -4z = -12z 18y + -12z = 0 Solving 18y + -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. 18y + -12z + 12z = 0 + 12z Combine like terms: -12z + 12z = 0 18y + 0 = 0 + 12z 18y = 0 + 12z Remove the zero: 18y = 12z Divide each side by '18'. y = 0.6666666667z Simplifying y = 0.6666666667z
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