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Simplifying z = 30 + -1(30 + -1z) + -1(30 + -1y + -1z) z = 30 + (30 * -1 + -1z * -1) + -1(30 + -1y + -1z) z = 30 + (-30 + 1z) + -1(30 + -1y + -1z) z = 30 + -30 + 1z + (30 * -1 + -1y * -1 + -1z * -1) z = 30 + -30 + 1z + (-30 + 1y + 1z) Reorder the terms: z = 30 + -30 + -30 + 1y + 1z + 1z Combine like terms: 30 + -30 = 0 z = 0 + -30 + 1y + 1z + 1z z = -30 + 1y + 1z + 1z Combine like terms: 1z + 1z = 2z z = -30 + 1y + 2z Solving z = -30 + 1y + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. z + -2z = -30 + 1y + 2z + -2z Combine like terms: z + -2z = -1z -1z = -30 + 1y + 2z + -2z Combine like terms: 2z + -2z = 0 -1z = -30 + 1y + 0 -1z = -30 + 1y Divide each side by '-1'. z = 30 + -1y Simplifying z = 30 + -1y
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