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Simplifying 7(5a + -1b) + -6(5b + -7a) = 0 (5a * 7 + -1b * 7) + -6(5b + -7a) = 0 (35a + -7b) + -6(5b + -7a) = 0 Reorder the terms: 35a + -7b + -6(-7a + 5b) = 0 35a + -7b + (-7a * -6 + 5b * -6) = 0 35a + -7b + (42a + -30b) = 0 Reorder the terms: 35a + 42a + -7b + -30b = 0 Combine like terms: 35a + 42a = 77a 77a + -7b + -30b = 0 Combine like terms: -7b + -30b = -37b 77a + -37b = 0 Solving 77a + -37b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '37b' to each side of the equation. 77a + -37b + 37b = 0 + 37b Combine like terms: -37b + 37b = 0 77a + 0 = 0 + 37b 77a = 0 + 37b Remove the zero: 77a = 37b Divide each side by '77'. a = 0.4805194805b Simplifying a = 0.4805194805b
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