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Simplifying 10(-3a + 3b + -4c) + -9(4a + -5b + 2c) = 0 (-3a * 10 + 3b * 10 + -4c * 10) + -9(4a + -5b + 2c) = 0 (-30a + 30b + -40c) + -9(4a + -5b + 2c) = 0 -30a + 30b + -40c + (4a * -9 + -5b * -9 + 2c * -9) = 0 -30a + 30b + -40c + (-36a + 45b + -18c) = 0 Reorder the terms: -30a + -36a + 30b + 45b + -40c + -18c = 0 Combine like terms: -30a + -36a = -66a -66a + 30b + 45b + -40c + -18c = 0 Combine like terms: 30b + 45b = 75b -66a + 75b + -40c + -18c = 0 Combine like terms: -40c + -18c = -58c -66a + 75b + -58c = 0 Solving -66a + 75b + -58c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-75b' to each side of the equation. -66a + 75b + -75b + -58c = 0 + -75b Combine like terms: 75b + -75b = 0 -66a + 0 + -58c = 0 + -75b -66a + -58c = 0 + -75b Remove the zero: -66a + -58c = -75b Add '58c' to each side of the equation. -66a + -58c + 58c = -75b + 58c Combine like terms: -58c + 58c = 0 -66a + 0 = -75b + 58c -66a = -75b + 58c Divide each side by '-66'. a = 1.136363636b + -0.8787878788c Simplifying a = 1.136363636b + -0.8787878788c
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