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Simplifying (2x + -6y + -2k) + -1(-7x + -5y + -4k) = 0 Reorder the terms: (-2k + 2x + -6y) + -1(-7x + -5y + -4k) = 0 Remove parenthesis around (-2k + 2x + -6y) -2k + 2x + -6y + -1(-7x + -5y + -4k) = 0 Reorder the terms: -2k + 2x + -6y + -1(-4k + -7x + -5y) = 0 -2k + 2x + -6y + (-4k * -1 + -7x * -1 + -5y * -1) = 0 -2k + 2x + -6y + (4k + 7x + 5y) = 0 Reorder the terms: -2k + 4k + 2x + 7x + -6y + 5y = 0 Combine like terms: -2k + 4k = 2k 2k + 2x + 7x + -6y + 5y = 0 Combine like terms: 2x + 7x = 9x 2k + 9x + -6y + 5y = 0 Combine like terms: -6y + 5y = -1y 2k + 9x + -1y = 0 Solving 2k + 9x + -1y = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-9x' to each side of the equation. 2k + 9x + -9x + -1y = 0 + -9x Combine like terms: 9x + -9x = 0 2k + 0 + -1y = 0 + -9x 2k + -1y = 0 + -9x Remove the zero: 2k + -1y = -9x Add 'y' to each side of the equation. 2k + -1y + y = -9x + y Combine like terms: -1y + y = 0 2k + 0 = -9x + y 2k = -9x + y Divide each side by '2'. k = -4.5x + 0.5y Simplifying k = -4.5x + 0.5y
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