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Simplifying 7(5a + -1b) + -6(8b + -8a) = 0 (5a * 7 + -1b * 7) + -6(8b + -8a) = 0 (35a + -7b) + -6(8b + -8a) = 0 Reorder the terms: 35a + -7b + -6(-8a + 8b) = 0 35a + -7b + (-8a * -6 + 8b * -6) = 0 35a + -7b + (48a + -48b) = 0 Reorder the terms: 35a + 48a + -7b + -48b = 0 Combine like terms: 35a + 48a = 83a 83a + -7b + -48b = 0 Combine like terms: -7b + -48b = -55b 83a + -55b = 0 Solving 83a + -55b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '55b' to each side of the equation. 83a + -55b + 55b = 0 + 55b Combine like terms: -55b + 55b = 0 83a + 0 = 0 + 55b 83a = 0 + 55b Remove the zero: 83a = 55b Divide each side by '83'. a = 0.6626506024b Simplifying a = 0.6626506024b
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