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Simplifying 10(3b + c + -7a) + -9(a + -8c + 6b) = 0 Reorder the terms: 10(-7a + 3b + c) + -9(a + -8c + 6b) = 0 (-7a * 10 + 3b * 10 + c * 10) + -9(a + -8c + 6b) = 0 (-70a + 30b + 10c) + -9(a + -8c + 6b) = 0 Reorder the terms: -70a + 30b + 10c + -9(a + 6b + -8c) = 0 -70a + 30b + 10c + (a * -9 + 6b * -9 + -8c * -9) = 0 -70a + 30b + 10c + (-9a + -54b + 72c) = 0 Reorder the terms: -70a + -9a + 30b + -54b + 10c + 72c = 0 Combine like terms: -70a + -9a = -79a -79a + 30b + -54b + 10c + 72c = 0 Combine like terms: 30b + -54b = -24b -79a + -24b + 10c + 72c = 0 Combine like terms: 10c + 72c = 82c -79a + -24b + 82c = 0 Solving -79a + -24b + 82c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '24b' to each side of the equation. -79a + -24b + 24b + 82c = 0 + 24b Combine like terms: -24b + 24b = 0 -79a + 0 + 82c = 0 + 24b -79a + 82c = 0 + 24b Remove the zero: -79a + 82c = 24b Add '-82c' to each side of the equation. -79a + 82c + -82c = 24b + -82c Combine like terms: 82c + -82c = 0 -79a + 0 = 24b + -82c -79a = 24b + -82c Divide each side by '-79'. a = -0.3037974684b + 1.037974684c Simplifying a = -0.3037974684b + 1.037974684c
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