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Simplifying 8(2a + -1b) + -1(2b + -4a) = 0 (2a * 8 + -1b * 8) + -1(2b + -4a) = 0 (16a + -8b) + -1(2b + -4a) = 0 Reorder the terms: 16a + -8b + -1(-4a + 2b) = 0 16a + -8b + (-4a * -1 + 2b * -1) = 0 16a + -8b + (4a + -2b) = 0 Reorder the terms: 16a + 4a + -8b + -2b = 0 Combine like terms: 16a + 4a = 20a 20a + -8b + -2b = 0 Combine like terms: -8b + -2b = -10b 20a + -10b = 0 Solving 20a + -10b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10b' to each side of the equation. 20a + -10b + 10b = 0 + 10b Combine like terms: -10b + 10b = 0 20a + 0 = 0 + 10b 20a = 0 + 10b Remove the zero: 20a = 10b Divide each side by '20'. a = 0.5b Simplifying a = 0.5b
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