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Simplifying (10k + 3r + -14z) + (15k + 17r + 19z) = 0 Remove parenthesis around (10k + 3r + -14z) 10k + 3r + -14z + (15k + 17r + 19z) = 0 Remove parenthesis around (15k + 17r + 19z) 10k + 3r + -14z + 15k + 17r + 19z = 0 Reorder the terms: 10k + 15k + 3r + 17r + -14z + 19z = 0 Combine like terms: 10k + 15k = 25k 25k + 3r + 17r + -14z + 19z = 0 Combine like terms: 3r + 17r = 20r 25k + 20r + -14z + 19z = 0 Combine like terms: -14z + 19z = 5z 25k + 20r + 5z = 0 Solving 25k + 20r + 5z = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-20r' to each side of the equation. 25k + 20r + -20r + 5z = 0 + -20r Combine like terms: 20r + -20r = 0 25k + 0 + 5z = 0 + -20r 25k + 5z = 0 + -20r Remove the zero: 25k + 5z = -20r Add '-5z' to each side of the equation. 25k + 5z + -5z = -20r + -5z Combine like terms: 5z + -5z = 0 25k + 0 = -20r + -5z 25k = -20r + -5z Divide each side by '25'. k = -0.8r + -0.2z Simplifying k = -0.8r + -0.2z
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