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Simplifying 5(5a + -1b) + -4(3b + -7a) = 0 (5a * 5 + -1b * 5) + -4(3b + -7a) = 0 (25a + -5b) + -4(3b + -7a) = 0 Reorder the terms: 25a + -5b + -4(-7a + 3b) = 0 25a + -5b + (-7a * -4 + 3b * -4) = 0 25a + -5b + (28a + -12b) = 0 Reorder the terms: 25a + 28a + -5b + -12b = 0 Combine like terms: 25a + 28a = 53a 53a + -5b + -12b = 0 Combine like terms: -5b + -12b = -17b 53a + -17b = 0 Solving 53a + -17b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '17b' to each side of the equation. 53a + -17b + 17b = 0 + 17b Combine like terms: -17b + 17b = 0 53a + 0 = 0 + 17b 53a = 0 + 17b Remove the zero: 53a = 17b Divide each side by '53'. a = 0.320754717b Simplifying a = 0.320754717b
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