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Simplifying 7(4a + -1b) + -3(4b + -5a) = 0 (4a * 7 + -1b * 7) + -3(4b + -5a) = 0 (28a + -7b) + -3(4b + -5a) = 0 Reorder the terms: 28a + -7b + -3(-5a + 4b) = 0 28a + -7b + (-5a * -3 + 4b * -3) = 0 28a + -7b + (15a + -12b) = 0 Reorder the terms: 28a + 15a + -7b + -12b = 0 Combine like terms: 28a + 15a = 43a 43a + -7b + -12b = 0 Combine like terms: -7b + -12b = -19b 43a + -19b = 0 Solving 43a + -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. 43a + -19b + 19b = 0 + 19b Combine like terms: -19b + 19b = 0 43a + 0 = 0 + 19b 43a = 0 + 19b Remove the zero: 43a = 19b Divide each side by '43'. a = 0.4418604651b Simplifying a = 0.4418604651b
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