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Simplifying 5(5a + -1b) + -7(7b + -8a) = 0 (5a * 5 + -1b * 5) + -7(7b + -8a) = 0 (25a + -5b) + -7(7b + -8a) = 0 Reorder the terms: 25a + -5b + -7(-8a + 7b) = 0 25a + -5b + (-8a * -7 + 7b * -7) = 0 25a + -5b + (56a + -49b) = 0 Reorder the terms: 25a + 56a + -5b + -49b = 0 Combine like terms: 25a + 56a = 81a 81a + -5b + -49b = 0 Combine like terms: -5b + -49b = -54b 81a + -54b = 0 Solving 81a + -54b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '54b' to each side of the equation. 81a + -54b + 54b = 0 + 54b Combine like terms: -54b + 54b = 0 81a + 0 = 0 + 54b 81a = 0 + 54b Remove the zero: 81a = 54b Divide each side by '81'. a = 0.6666666667b Simplifying a = 0.6666666667b
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