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Simplifying 7(8a + -1b) + -5(7b + -5a) = 0 (8a * 7 + -1b * 7) + -5(7b + -5a) = 0 (56a + -7b) + -5(7b + -5a) = 0 Reorder the terms: 56a + -7b + -5(-5a + 7b) = 0 56a + -7b + (-5a * -5 + 7b * -5) = 0 56a + -7b + (25a + -35b) = 0 Reorder the terms: 56a + 25a + -7b + -35b = 0 Combine like terms: 56a + 25a = 81a 81a + -7b + -35b = 0 Combine like terms: -7b + -35b = -42b 81a + -42b = 0 Solving 81a + -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. 81a + -42b + 42b = 0 + 42b Combine like terms: -42b + 42b = 0 81a + 0 = 0 + 42b 81a = 0 + 42b Remove the zero: 81a = 42b Divide each side by '81'. a = 0.5185185185b Simplifying a = 0.5185185185b
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