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Simplifying (1 + -1x) * x + (1 + -1x) * y + 3 + -1k = 0 Reorder the terms for easier multiplication: x(1 + -1x) + (1 + -1x) * y + 3 + -1k = 0 (1 * x + -1x * x) + (1 + -1x) * y + 3 + -1k = 0 (1x + -1x2) + (1 + -1x) * y + 3 + -1k = 0 Reorder the terms for easier multiplication: 1x + -1x2 + y(1 + -1x) + 3 + -1k = 0 1x + -1x2 + (1 * y + -1x * y) + 3 + -1k = 0 Reorder the terms: 1x + -1x2 + (-1xy + 1y) + 3 + -1k = 0 1x + -1x2 + (-1xy + 1y) + 3 + -1k = 0 Reorder the terms: 3 + -1k + 1x + -1xy + -1x2 + 1y = 0 Solving 3 + -1k + 1x + -1xy + -1x2 + 1y = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -1k + 1x + -1xy + -1x2 + -3 + 1y = 0 + -3 Reorder the terms: 3 + -3 + -1k + 1x + -1xy + -1x2 + 1y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1k + 1x + -1xy + -1x2 + 1y = 0 + -3 -1k + 1x + -1xy + -1x2 + 1y = 0 + -3 Combine like terms: 0 + -3 = -3 -1k + 1x + -1xy + -1x2 + 1y = -3 Add '-1x' to each side of the equation. -1k + 1x + -1xy + -1x2 + -1x + 1y = -3 + -1x Reorder the terms: -1k + 1x + -1x + -1xy + -1x2 + 1y = -3 + -1x Combine like terms: 1x + -1x = 0 -1k + 0 + -1xy + -1x2 + 1y = -3 + -1x -1k + -1xy + -1x2 + 1y = -3 + -1x Add 'xy' to each side of the equation. -1k + -1xy + -1x2 + xy + 1y = -3 + -1x + xy Reorder the terms: -1k + -1xy + xy + -1x2 + 1y = -3 + -1x + xy Combine like terms: -1xy + xy = 0 -1k + 0 + -1x2 + 1y = -3 + -1x + xy -1k + -1x2 + 1y = -3 + -1x + xy Add 'x2' to each side of the equation. -1k + -1x2 + x2 + 1y = -3 + -1x + xy + x2 Combine like terms: -1x2 + x2 = 0 -1k + 0 + 1y = -3 + -1x + xy + x2 -1k + 1y = -3 + -1x + xy + x2 Add '-1y' to each side of the equation. -1k + 1y + -1y = -3 + -1x + xy + x2 + -1y Combine like terms: 1y + -1y = 0 -1k + 0 = -3 + -1x + xy + x2 + -1y -1k = -3 + -1x + xy + x2 + -1y Divide each side by '-1'. k = 3 + x + -1xy + -1x2 + y Simplifying k = 3 + x + -1xy + -1x2 + y
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