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Simplifying 4r + 6s + -3t + 2r + 5t + -1s = 0 Reorder the terms: 4r + 2r + 6s + -1s + -3t + 5t = 0 Combine like terms: 4r + 2r = 6r 6r + 6s + -1s + -3t + 5t = 0 Combine like terms: 6s + -1s = 5s 6r + 5s + -3t + 5t = 0 Combine like terms: -3t + 5t = 2t 6r + 5s + 2t = 0 Solving 6r + 5s + 2t = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5s' to each side of the equation. 6r + 5s + -5s + 2t = 0 + -5s Combine like terms: 5s + -5s = 0 6r + 0 + 2t = 0 + -5s 6r + 2t = 0 + -5s Remove the zero: 6r + 2t = -5s Add '-2t' to each side of the equation. 6r + 2t + -2t = -5s + -2t Combine like terms: 2t + -2t = 0 6r + 0 = -5s + -2t 6r = -5s + -2t Divide each side by '6'. r = -0.8333333333s + -0.3333333333t Simplifying r = -0.8333333333s + -0.3333333333t
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