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Simplifying 3(3a + -1b) + -7(2b + -6a) = 0 (3a * 3 + -1b * 3) + -7(2b + -6a) = 0 (9a + -3b) + -7(2b + -6a) = 0 Reorder the terms: 9a + -3b + -7(-6a + 2b) = 0 9a + -3b + (-6a * -7 + 2b * -7) = 0 9a + -3b + (42a + -14b) = 0 Reorder the terms: 9a + 42a + -3b + -14b = 0 Combine like terms: 9a + 42a = 51a 51a + -3b + -14b = 0 Combine like terms: -3b + -14b = -17b 51a + -17b = 0 Solving 51a + -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. 51a + -17b + 17b = 0 + 17b Combine like terms: -17b + 17b = 0 51a + 0 = 0 + 17b 51a = 0 + 17b Remove the zero: 51a = 17b Divide each side by '51'. a = 0.3333333333b Simplifying a = 0.3333333333b
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