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Simplifying 5(8a + -1b) + -8(8b + -5a) = 0 (8a * 5 + -1b * 5) + -8(8b + -5a) = 0 (40a + -5b) + -8(8b + -5a) = 0 Reorder the terms: 40a + -5b + -8(-5a + 8b) = 0 40a + -5b + (-5a * -8 + 8b * -8) = 0 40a + -5b + (40a + -64b) = 0 Reorder the terms: 40a + 40a + -5b + -64b = 0 Combine like terms: 40a + 40a = 80a 80a + -5b + -64b = 0 Combine like terms: -5b + -64b = -69b 80a + -69b = 0 Solving 80a + -69b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '69b' to each side of the equation. 80a + -69b + 69b = 0 + 69b Combine like terms: -69b + 69b = 0 80a + 0 = 0 + 69b 80a = 0 + 69b Remove the zero: 80a = 69b Divide each side by '80'. a = 0.8625b Simplifying a = 0.8625b
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