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Simplifying 10(-2a + 2b + -4c) + -9(3a + -6b + 3c) = 0 (-2a * 10 + 2b * 10 + -4c * 10) + -9(3a + -6b + 3c) = 0 (-20a + 20b + -40c) + -9(3a + -6b + 3c) = 0 -20a + 20b + -40c + (3a * -9 + -6b * -9 + 3c * -9) = 0 -20a + 20b + -40c + (-27a + 54b + -27c) = 0 Reorder the terms: -20a + -27a + 20b + 54b + -40c + -27c = 0 Combine like terms: -20a + -27a = -47a -47a + 20b + 54b + -40c + -27c = 0 Combine like terms: 20b + 54b = 74b -47a + 74b + -40c + -27c = 0 Combine like terms: -40c + -27c = -67c -47a + 74b + -67c = 0 Solving -47a + 74b + -67c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-74b' to each side of the equation. -47a + 74b + -74b + -67c = 0 + -74b Combine like terms: 74b + -74b = 0 -47a + 0 + -67c = 0 + -74b -47a + -67c = 0 + -74b Remove the zero: -47a + -67c = -74b Add '67c' to each side of the equation. -47a + -67c + 67c = -74b + 67c Combine like terms: -67c + 67c = 0 -47a + 0 = -74b + 67c -47a = -74b + 67c Divide each side by '-47'. a = 1.574468085b + -1.425531915c Simplifying a = 1.574468085b + -1.425531915c
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