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Simplifying 7(2a + -1b) + -3(4b + -7a) = 0 (2a * 7 + -1b * 7) + -3(4b + -7a) = 0 (14a + -7b) + -3(4b + -7a) = 0 Reorder the terms: 14a + -7b + -3(-7a + 4b) = 0 14a + -7b + (-7a * -3 + 4b * -3) = 0 14a + -7b + (21a + -12b) = 0 Reorder the terms: 14a + 21a + -7b + -12b = 0 Combine like terms: 14a + 21a = 35a 35a + -7b + -12b = 0 Combine like terms: -7b + -12b = -19b 35a + -19b = 0 Solving 35a + -19b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '19b' to each side of the equation. 35a + -19b + 19b = 0 + 19b Combine like terms: -19b + 19b = 0 35a + 0 = 0 + 19b 35a = 0 + 19b Remove the zero: 35a = 19b Divide each side by '35'. a = 0.5428571429b Simplifying a = 0.5428571429b
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