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Simplifying (5r + 7s + -1t) + -1(3r + t) + -1(6s + t) = 0 Remove parenthesis around (5r + 7s + -1t) 5r + 7s + -1t + -1(3r + t) + -1(6s + t) = 0 5r + 7s + -1t + (3r * -1 + t * -1) + -1(6s + t) = 0 5r + 7s + -1t + (-3r + -1t) + -1(6s + t) = 0 5r + 7s + -1t + -3r + -1t + (6s * -1 + t * -1) = 0 5r + 7s + -1t + -3r + -1t + (-6s + -1t) = 0 Reorder the terms: 5r + -3r + 7s + -6s + -1t + -1t + -1t = 0 Combine like terms: 5r + -3r = 2r 2r + 7s + -6s + -1t + -1t + -1t = 0 Combine like terms: 7s + -6s = 1s 2r + 1s + -1t + -1t + -1t = 0 Combine like terms: -1t + -1t = -2t 2r + 1s + -2t + -1t = 0 Combine like terms: -2t + -1t = -3t 2r + 1s + -3t = 0 Solving 2r + 1s + -3t = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1s' to each side of the equation. 2r + 1s + -1s + -3t = 0 + -1s Combine like terms: 1s + -1s = 0 2r + 0 + -3t = 0 + -1s 2r + -3t = 0 + -1s Remove the zero: 2r + -3t = -1s Add '3t' to each side of the equation. 2r + -3t + 3t = -1s + 3t Combine like terms: -3t + 3t = 0 2r + 0 = -1s + 3t 2r = -1s + 3t Divide each side by '2'. r = -0.5s + 1.5t Simplifying r = -0.5s + 1.5t
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