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