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Simplifying 7(2a + -1b) + -5(3b + -5a) = 0 (2a * 7 + -1b * 7) + -5(3b + -5a) = 0 (14a + -7b) + -5(3b + -5a) = 0 Reorder the terms: 14a + -7b + -5(-5a + 3b) = 0 14a + -7b + (-5a * -5 + 3b * -5) = 0 14a + -7b + (25a + -15b) = 0 Reorder the terms: 14a + 25a + -7b + -15b = 0 Combine like terms: 14a + 25a = 39a 39a + -7b + -15b = 0 Combine like terms: -7b + -15b = -22b 39a + -22b = 0 Solving 39a + -22b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '22b' to each side of the equation. 39a + -22b + 22b = 0 + 22b Combine like terms: -22b + 22b = 0 39a + 0 = 0 + 22b 39a = 0 + 22b Remove the zero: 39a = 22b Divide each side by '39'. a = 0.5641025641b Simplifying a = 0.5641025641b
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