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Simplifying 5(3a + -1b) + -7(3b + -7a) = 0 (3a * 5 + -1b * 5) + -7(3b + -7a) = 0 (15a + -5b) + -7(3b + -7a) = 0 Reorder the terms: 15a + -5b + -7(-7a + 3b) = 0 15a + -5b + (-7a * -7 + 3b * -7) = 0 15a + -5b + (49a + -21b) = 0 Reorder the terms: 15a + 49a + -5b + -21b = 0 Combine like terms: 15a + 49a = 64a 64a + -5b + -21b = 0 Combine like terms: -5b + -21b = -26b 64a + -26b = 0 Solving 64a + -26b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '26b' to each side of the equation. 64a + -26b + 26b = 0 + 26b Combine like terms: -26b + 26b = 0 64a + 0 = 0 + 26b 64a = 0 + 26b Remove the zero: 64a = 26b Divide each side by '64'. a = 0.40625b Simplifying a = 0.40625b
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