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Simplifying 2(9b + -13a) + 5(2a + -3b) = 0 Reorder the terms: 2(-13a + 9b) + 5(2a + -3b) = 0 (-13a * 2 + 9b * 2) + 5(2a + -3b) = 0 (-26a + 18b) + 5(2a + -3b) = 0 -26a + 18b + (2a * 5 + -3b * 5) = 0 -26a + 18b + (10a + -15b) = 0 Reorder the terms: -26a + 10a + 18b + -15b = 0 Combine like terms: -26a + 10a = -16a -16a + 18b + -15b = 0 Combine like terms: 18b + -15b = 3b -16a + 3b = 0 Solving -16a + 3b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. -16a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 -16a + 0 = 0 + -3b -16a = 0 + -3b Remove the zero: -16a = -3b Divide each side by '-16'. a = 0.1875b Simplifying a = 0.1875b
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