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Simplifying 3(9a + -1b) + -6(b + -9a) = 0 (9a * 3 + -1b * 3) + -6(b + -9a) = 0 (27a + -3b) + -6(b + -9a) = 0 Reorder the terms: 27a + -3b + -6(-9a + b) = 0 27a + -3b + (-9a * -6 + b * -6) = 0 27a + -3b + (54a + -6b) = 0 Reorder the terms: 27a + 54a + -3b + -6b = 0 Combine like terms: 27a + 54a = 81a 81a + -3b + -6b = 0 Combine like terms: -3b + -6b = -9b 81a + -9b = 0 Solving 81a + -9b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '9b' to each side of the equation. 81a + -9b + 9b = 0 + 9b Combine like terms: -9b + 9b = 0 81a + 0 = 0 + 9b 81a = 0 + 9b Remove the zero: 81a = 9b Divide each side by '81'. a = 0.1111111111b Simplifying a = 0.1111111111b
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