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Simplifying 3(5a + -1b) + -7(4b + -7a) = 0 (5a * 3 + -1b * 3) + -7(4b + -7a) = 0 (15a + -3b) + -7(4b + -7a) = 0 Reorder the terms: 15a + -3b + -7(-7a + 4b) = 0 15a + -3b + (-7a * -7 + 4b * -7) = 0 15a + -3b + (49a + -28b) = 0 Reorder the terms: 15a + 49a + -3b + -28b = 0 Combine like terms: 15a + 49a = 64a 64a + -3b + -28b = 0 Combine like terms: -3b + -28b = -31b 64a + -31b = 0 Solving 64a + -31b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '31b' to each side of the equation. 64a + -31b + 31b = 0 + 31b Combine like terms: -31b + 31b = 0 64a + 0 = 0 + 31b 64a = 0 + 31b Remove the zero: 64a = 31b Divide each side by '64'. a = 0.484375b Simplifying a = 0.484375b
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