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Simplifying 11(-2a + 2b + -3c) + -9(3a + -5b + 3c) = 0 (-2a * 11 + 2b * 11 + -3c * 11) + -9(3a + -5b + 3c) = 0 (-22a + 22b + -33c) + -9(3a + -5b + 3c) = 0 -22a + 22b + -33c + (3a * -9 + -5b * -9 + 3c * -9) = 0 -22a + 22b + -33c + (-27a + 45b + -27c) = 0 Reorder the terms: -22a + -27a + 22b + 45b + -33c + -27c = 0 Combine like terms: -22a + -27a = -49a -49a + 22b + 45b + -33c + -27c = 0 Combine like terms: 22b + 45b = 67b -49a + 67b + -33c + -27c = 0 Combine like terms: -33c + -27c = -60c -49a + 67b + -60c = 0 Solving -49a + 67b + -60c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-67b' to each side of the equation. -49a + 67b + -67b + -60c = 0 + -67b Combine like terms: 67b + -67b = 0 -49a + 0 + -60c = 0 + -67b -49a + -60c = 0 + -67b Remove the zero: -49a + -60c = -67b Add '60c' to each side of the equation. -49a + -60c + 60c = -67b + 60c Combine like terms: -60c + 60c = 0 -49a + 0 = -67b + 60c -49a = -67b + 60c Divide each side by '-49'. a = 1.367346939b + -1.224489796c Simplifying a = 1.367346939b + -1.224489796c
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