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Simplifying 3q + 4r + -1s + 5q + -6r + 2s = 0 Reorder the terms: 3q + 5q + 4r + -6r + -1s + 2s = 0 Combine like terms: 3q + 5q = 8q 8q + 4r + -6r + -1s + 2s = 0 Combine like terms: 4r + -6r = -2r 8q + -2r + -1s + 2s = 0 Combine like terms: -1s + 2s = 1s 8q + -2r + 1s = 0 Solving 8q + -2r + 1s = 0 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2r' to each side of the equation. 8q + -2r + 2r + 1s = 0 + 2r Combine like terms: -2r + 2r = 0 8q + 0 + 1s = 0 + 2r 8q + 1s = 0 + 2r Remove the zero: 8q + 1s = 2r Add '-1s' to each side of the equation. 8q + 1s + -1s = 2r + -1s Combine like terms: 1s + -1s = 0 8q + 0 = 2r + -1s 8q = 2r + -1s Divide each side by '8'. q = 0.25r + -0.125s Simplifying q = 0.25r + -0.125s
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