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Simplifying 5(9a + -1b) + -9(b + -9a) = 0 (9a * 5 + -1b * 5) + -9(b + -9a) = 0 (45a + -5b) + -9(b + -9a) = 0 Reorder the terms: 45a + -5b + -9(-9a + b) = 0 45a + -5b + (-9a * -9 + b * -9) = 0 45a + -5b + (81a + -9b) = 0 Reorder the terms: 45a + 81a + -5b + -9b = 0 Combine like terms: 45a + 81a = 126a 126a + -5b + -9b = 0 Combine like terms: -5b + -9b = -14b 126a + -14b = 0 Solving 126a + -14b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '14b' to each side of the equation. 126a + -14b + 14b = 0 + 14b Combine like terms: -14b + 14b = 0 126a + 0 = 0 + 14b 126a = 0 + 14b Remove the zero: 126a = 14b Divide each side by '126'. a = 0.1111111111b Simplifying a = 0.1111111111b
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