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Simplifying x + 2y + -4z + 3r + -1s = 0 Reorder the terms: 3r + -1s + x + 2y + -4z = 0 Solving 3r + -1s + x + 2y + -4z = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add 's' to each side of the equation. 3r + -1s + x + 2y + s + -4z = 0 + s Reorder the terms: 3r + -1s + s + x + 2y + -4z = 0 + s Combine like terms: -1s + s = 0 3r + 0 + x + 2y + -4z = 0 + s 3r + x + 2y + -4z = 0 + s Remove the zero: 3r + x + 2y + -4z = s Add '-1x' to each side of the equation. 3r + x + 2y + -1x + -4z = s + -1x Reorder the terms: 3r + x + -1x + 2y + -4z = s + -1x Combine like terms: x + -1x = 0 3r + 0 + 2y + -4z = s + -1x 3r + 2y + -4z = s + -1x Add '-2y' to each side of the equation. 3r + 2y + -2y + -4z = s + -1x + -2y Combine like terms: 2y + -2y = 0 3r + 0 + -4z = s + -1x + -2y 3r + -4z = s + -1x + -2y Add '4z' to each side of the equation. 3r + -4z + 4z = s + -1x + -2y + 4z Combine like terms: -4z + 4z = 0 3r + 0 = s + -1x + -2y + 4z 3r = s + -1x + -2y + 4z Divide each side by '3'. r = 0.3333333333s + -0.3333333333x + -0.6666666667y + 1.333333333z Simplifying r = 0.3333333333s + -0.3333333333x + -0.6666666667y + 1.333333333z
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