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Simplifying 7(5a + -1b) + -5(7b + -8a) = 0 (5a * 7 + -1b * 7) + -5(7b + -8a) = 0 (35a + -7b) + -5(7b + -8a) = 0 Reorder the terms: 35a + -7b + -5(-8a + 7b) = 0 35a + -7b + (-8a * -5 + 7b * -5) = 0 35a + -7b + (40a + -35b) = 0 Reorder the terms: 35a + 40a + -7b + -35b = 0 Combine like terms: 35a + 40a = 75a 75a + -7b + -35b = 0 Combine like terms: -7b + -35b = -42b 75a + -42b = 0 Solving 75a + -42b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '42b' to each side of the equation. 75a + -42b + 42b = 0 + 42b Combine like terms: -42b + 42b = 0 75a + 0 = 0 + 42b 75a = 0 + 42b Remove the zero: 75a = 42b Divide each side by '75'. a = 0.56b Simplifying a = 0.56b
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