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Simplifying 11(-3a + 3b + -3c) + -9(3a + -7b + 3c) = 0 (-3a * 11 + 3b * 11 + -3c * 11) + -9(3a + -7b + 3c) = 0 (-33a + 33b + -33c) + -9(3a + -7b + 3c) = 0 -33a + 33b + -33c + (3a * -9 + -7b * -9 + 3c * -9) = 0 -33a + 33b + -33c + (-27a + 63b + -27c) = 0 Reorder the terms: -33a + -27a + 33b + 63b + -33c + -27c = 0 Combine like terms: -33a + -27a = -60a -60a + 33b + 63b + -33c + -27c = 0 Combine like terms: 33b + 63b = 96b -60a + 96b + -33c + -27c = 0 Combine like terms: -33c + -27c = -60c -60a + 96b + -60c = 0 Solving -60a + 96b + -60c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-96b' to each side of the equation. -60a + 96b + -96b + -60c = 0 + -96b Combine like terms: 96b + -96b = 0 -60a + 0 + -60c = 0 + -96b -60a + -60c = 0 + -96b Remove the zero: -60a + -60c = -96b Add '60c' to each side of the equation. -60a + -60c + 60c = -96b + 60c Combine like terms: -60c + 60c = 0 -60a + 0 = -96b + 60c -60a = -96b + 60c Divide each side by '-60'. a = 1.6b + -1c Simplifying a = 1.6b + -1c
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