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Simplifying 5(2a + -1b) + -7(6b + -7a) = 0 (2a * 5 + -1b * 5) + -7(6b + -7a) = 0 (10a + -5b) + -7(6b + -7a) = 0 Reorder the terms: 10a + -5b + -7(-7a + 6b) = 0 10a + -5b + (-7a * -7 + 6b * -7) = 0 10a + -5b + (49a + -42b) = 0 Reorder the terms: 10a + 49a + -5b + -42b = 0 Combine like terms: 10a + 49a = 59a 59a + -5b + -42b = 0 Combine like terms: -5b + -42b = -47b 59a + -47b = 0 Solving 59a + -47b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '47b' to each side of the equation. 59a + -47b + 47b = 0 + 47b Combine like terms: -47b + 47b = 0 59a + 0 = 0 + 47b 59a = 0 + 47b Remove the zero: 59a = 47b Divide each side by '59'. a = 0.7966101695b Simplifying a = 0.7966101695b
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