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Simplifying 5(2a + -1b) + -7(2b + -8a) = 0 (2a * 5 + -1b * 5) + -7(2b + -8a) = 0 (10a + -5b) + -7(2b + -8a) = 0 Reorder the terms: 10a + -5b + -7(-8a + 2b) = 0 10a + -5b + (-8a * -7 + 2b * -7) = 0 10a + -5b + (56a + -14b) = 0 Reorder the terms: 10a + 56a + -5b + -14b = 0 Combine like terms: 10a + 56a = 66a 66a + -5b + -14b = 0 Combine like terms: -5b + -14b = -19b 66a + -19b = 0 Solving 66a + -19b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '19b' to each side of the equation. 66a + -19b + 19b = 0 + 19b Combine like terms: -19b + 19b = 0 66a + 0 = 0 + 19b 66a = 0 + 19b Remove the zero: 66a = 19b Divide each side by '66'. a = 0.2878787879b Simplifying a = 0.2878787879b
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