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Simplifying 10r + -3s + -1(r + -2s) + -1(-3s + 5t) = 0 10r + -3s + (r * -1 + -2s * -1) + -1(-3s + 5t) = 0 10r + -3s + (-1r + 2s) + -1(-3s + 5t) = 0 10r + -3s + -1r + 2s + (-3s * -1 + 5t * -1) = 0 10r + -3s + -1r + 2s + (3s + -5t) = 0 Reorder the terms: 10r + -1r + -3s + 2s + 3s + -5t = 0 Combine like terms: 10r + -1r = 9r 9r + -3s + 2s + 3s + -5t = 0 Combine like terms: -3s + 2s = -1s 9r + -1s + 3s + -5t = 0 Combine like terms: -1s + 3s = 2s 9r + 2s + -5t = 0 Solving 9r + 2s + -5t = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2s' to each side of the equation. 9r + 2s + -2s + -5t = 0 + -2s Combine like terms: 2s + -2s = 0 9r + 0 + -5t = 0 + -2s 9r + -5t = 0 + -2s Remove the zero: 9r + -5t = -2s Add '5t' to each side of the equation. 9r + -5t + 5t = -2s + 5t Combine like terms: -5t + 5t = 0 9r + 0 = -2s + 5t 9r = -2s + 5t Divide each side by '9'. r = -0.2222222222s + 0.5555555556t Simplifying r = -0.2222222222s + 0.5555555556t
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