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Simplifying 5(8a + -1b) + -7(8b + -6a) = 0 (8a * 5 + -1b * 5) + -7(8b + -6a) = 0 (40a + -5b) + -7(8b + -6a) = 0 Reorder the terms: 40a + -5b + -7(-6a + 8b) = 0 40a + -5b + (-6a * -7 + 8b * -7) = 0 40a + -5b + (42a + -56b) = 0 Reorder the terms: 40a + 42a + -5b + -56b = 0 Combine like terms: 40a + 42a = 82a 82a + -5b + -56b = 0 Combine like terms: -5b + -56b = -61b 82a + -61b = 0 Solving 82a + -61b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '61b' to each side of the equation. 82a + -61b + 61b = 0 + 61b Combine like terms: -61b + 61b = 0 82a + 0 = 0 + 61b 82a = 0 + 61b Remove the zero: 82a = 61b Divide each side by '82'. a = 0.743902439b Simplifying a = 0.743902439b
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