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Simplifying 5(2a + -1b) + -3(6b + -7a) = 0 (2a * 5 + -1b * 5) + -3(6b + -7a) = 0 (10a + -5b) + -3(6b + -7a) = 0 Reorder the terms: 10a + -5b + -3(-7a + 6b) = 0 10a + -5b + (-7a * -3 + 6b * -3) = 0 10a + -5b + (21a + -18b) = 0 Reorder the terms: 10a + 21a + -5b + -18b = 0 Combine like terms: 10a + 21a = 31a 31a + -5b + -18b = 0 Combine like terms: -5b + -18b = -23b 31a + -23b = 0 Solving 31a + -23b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '23b' to each side of the equation. 31a + -23b + 23b = 0 + 23b Combine like terms: -23b + 23b = 0 31a + 0 = 0 + 23b 31a = 0 + 23b Remove the zero: 31a = 23b Divide each side by '31'. a = 0.7419354839b Simplifying a = 0.7419354839b
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