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Simplifying 5(2a + -1b) + 2(3b + -4a) = 0 (2a * 5 + -1b * 5) + 2(3b + -4a) = 0 (10a + -5b) + 2(3b + -4a) = 0 Reorder the terms: 10a + -5b + 2(-4a + 3b) = 0 10a + -5b + (-4a * 2 + 3b * 2) = 0 10a + -5b + (-8a + 6b) = 0 Reorder the terms: 10a + -8a + -5b + 6b = 0 Combine like terms: 10a + -8a = 2a 2a + -5b + 6b = 0 Combine like terms: -5b + 6b = 1b 2a + 1b = 0 Solving 2a + 1b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 2a + 1b + -1b = 0 + -1b Combine like terms: 1b + -1b = 0 2a + 0 = 0 + -1b 2a = 0 + -1b Remove the zero: 2a = -1b Divide each side by '2'. a = -0.5b Simplifying a = -0.5b
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