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Simplifying 5k + -2y + 4z + -9k + -3y + -6z = 0 Reorder the terms: 5k + -9k + -2y + -3y + 4z + -6z = 0 Combine like terms: 5k + -9k = -4k -4k + -2y + -3y + 4z + -6z = 0 Combine like terms: -2y + -3y = -5y -4k + -5y + 4z + -6z = 0 Combine like terms: 4z + -6z = -2z -4k + -5y + -2z = 0 Solving -4k + -5y + -2z = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '5y' to each side of the equation. -4k + -5y + 5y + -2z = 0 + 5y Combine like terms: -5y + 5y = 0 -4k + 0 + -2z = 0 + 5y -4k + -2z = 0 + 5y Remove the zero: -4k + -2z = 5y Add '2z' to each side of the equation. -4k + -2z + 2z = 5y + 2z Combine like terms: -2z + 2z = 0 -4k + 0 = 5y + 2z -4k = 5y + 2z Divide each side by '-4'. k = -1.25y + -0.5z Simplifying k = -1.25y + -0.5z
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