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Simplifying 8(4a + -1b) + -5(7b + -8a) = 0 (4a * 8 + -1b * 8) + -5(7b + -8a) = 0 (32a + -8b) + -5(7b + -8a) = 0 Reorder the terms: 32a + -8b + -5(-8a + 7b) = 0 32a + -8b + (-8a * -5 + 7b * -5) = 0 32a + -8b + (40a + -35b) = 0 Reorder the terms: 32a + 40a + -8b + -35b = 0 Combine like terms: 32a + 40a = 72a 72a + -8b + -35b = 0 Combine like terms: -8b + -35b = -43b 72a + -43b = 0 Solving 72a + -43b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '43b' to each side of the equation. 72a + -43b + 43b = 0 + 43b Combine like terms: -43b + 43b = 0 72a + 0 = 0 + 43b 72a = 0 + 43b Remove the zero: 72a = 43b Divide each side by '72'. a = 0.5972222222b Simplifying a = 0.5972222222b
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