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Simplifying 5(6a + -1b) + -7(5b + -7a) = 0 (6a * 5 + -1b * 5) + -7(5b + -7a) = 0 (30a + -5b) + -7(5b + -7a) = 0 Reorder the terms: 30a + -5b + -7(-7a + 5b) = 0 30a + -5b + (-7a * -7 + 5b * -7) = 0 30a + -5b + (49a + -35b) = 0 Reorder the terms: 30a + 49a + -5b + -35b = 0 Combine like terms: 30a + 49a = 79a 79a + -5b + -35b = 0 Combine like terms: -5b + -35b = -40b 79a + -40b = 0 Solving 79a + -40b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '40b' to each side of the equation. 79a + -40b + 40b = 0 + 40b Combine like terms: -40b + 40b = 0 79a + 0 = 0 + 40b 79a = 0 + 40b Remove the zero: 79a = 40b Divide each side by '79'. a = 0.5063291139b Simplifying a = 0.5063291139b
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