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Simplifying 10(-3a + 2b + -4c) + -9(3a + -5b + 3c) = 0 (-3a * 10 + 2b * 10 + -4c * 10) + -9(3a + -5b + 3c) = 0 (-30a + 20b + -40c) + -9(3a + -5b + 3c) = 0 -30a + 20b + -40c + (3a * -9 + -5b * -9 + 3c * -9) = 0 -30a + 20b + -40c + (-27a + 45b + -27c) = 0 Reorder the terms: -30a + -27a + 20b + 45b + -40c + -27c = 0 Combine like terms: -30a + -27a = -57a -57a + 20b + 45b + -40c + -27c = 0 Combine like terms: 20b + 45b = 65b -57a + 65b + -40c + -27c = 0 Combine like terms: -40c + -27c = -67c -57a + 65b + -67c = 0 Solving -57a + 65b + -67c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-65b' to each side of the equation. -57a + 65b + -65b + -67c = 0 + -65b Combine like terms: 65b + -65b = 0 -57a + 0 + -67c = 0 + -65b -57a + -67c = 0 + -65b Remove the zero: -57a + -67c = -65b Add '67c' to each side of the equation. -57a + -67c + 67c = -65b + 67c Combine like terms: -67c + 67c = 0 -57a + 0 = -65b + 67c -57a = -65b + 67c Divide each side by '-57'. a = 1.140350877b + -1.175438596c Simplifying a = 1.140350877b + -1.175438596c
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