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Simplifying 8(5a + -1b) + -5(3b + -7a) = 0 (5a * 8 + -1b * 8) + -5(3b + -7a) = 0 (40a + -8b) + -5(3b + -7a) = 0 Reorder the terms: 40a + -8b + -5(-7a + 3b) = 0 40a + -8b + (-7a * -5 + 3b * -5) = 0 40a + -8b + (35a + -15b) = 0 Reorder the terms: 40a + 35a + -8b + -15b = 0 Combine like terms: 40a + 35a = 75a 75a + -8b + -15b = 0 Combine like terms: -8b + -15b = -23b 75a + -23b = 0 Solving 75a + -23b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '23b' to each side of the equation. 75a + -23b + 23b = 0 + 23b Combine like terms: -23b + 23b = 0 75a + 0 = 0 + 23b 75a = 0 + 23b Remove the zero: 75a = 23b Divide each side by '75'. a = 0.3066666667b Simplifying a = 0.3066666667b
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