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Simplifying (10a + 3c + 9b) + (4b + 5c + 9a) = 0 Reorder the terms: (10a + 9b + 3c) + (4b + 5c + 9a) = 0 Remove parenthesis around (10a + 9b + 3c) 10a + 9b + 3c + (4b + 5c + 9a) = 0 Reorder the terms: 10a + 9b + 3c + (9a + 4b + 5c) = 0 Remove parenthesis around (9a + 4b + 5c) 10a + 9b + 3c + 9a + 4b + 5c = 0 Reorder the terms: 10a + 9a + 9b + 4b + 3c + 5c = 0 Combine like terms: 10a + 9a = 19a 19a + 9b + 4b + 3c + 5c = 0 Combine like terms: 9b + 4b = 13b 19a + 13b + 3c + 5c = 0 Combine like terms: 3c + 5c = 8c 19a + 13b + 8c = 0 Solving 19a + 13b + 8c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-13b' to each side of the equation. 19a + 13b + -13b + 8c = 0 + -13b Combine like terms: 13b + -13b = 0 19a + 0 + 8c = 0 + -13b 19a + 8c = 0 + -13b Remove the zero: 19a + 8c = -13b Add '-8c' to each side of the equation. 19a + 8c + -8c = -13b + -8c Combine like terms: 8c + -8c = 0 19a + 0 = -13b + -8c 19a = -13b + -8c Divide each side by '19'. a = -0.6842105263b + -0.4210526316c Simplifying a = -0.6842105263b + -0.4210526316c
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