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Simplifying (k + 1) * x + (k + -2) * y + -1 = 0 Reorder the terms: (1 + k) * x + (k + -2) * y + -1 = 0 Reorder the terms for easier multiplication: x(1 + k) + (k + -2) * y + -1 = 0 (1 * x + k * x) + (k + -2) * y + -1 = 0 Reorder the terms: (kx + 1x) + (k + -2) * y + -1 = 0 (kx + 1x) + (k + -2) * y + -1 = 0 Reorder the terms: kx + 1x + (-2 + k) * y + -1 = 0 Reorder the terms for easier multiplication: kx + 1x + y(-2 + k) + -1 = 0 kx + 1x + (-2 * y + k * y) + -1 = 0 Reorder the terms: kx + 1x + (ky + -2y) + -1 = 0 kx + 1x + (ky + -2y) + -1 = 0 Reorder the terms: -1 + kx + ky + 1x + -2y = 0 Solving -1 + kx + ky + 1x + -2y = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1' to each side of the equation. -1 + kx + ky + 1x + 1 + -2y = 0 + 1 Reorder the terms: -1 + 1 + kx + ky + 1x + -2y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + kx + ky + 1x + -2y = 0 + 1 kx + ky + 1x + -2y = 0 + 1 Combine like terms: 0 + 1 = 1 kx + ky + 1x + -2y = 1 Add '-1x' to each side of the equation. kx + ky + 1x + -1x + -2y = 1 + -1x Combine like terms: 1x + -1x = 0 kx + ky + 0 + -2y = 1 + -1x kx + ky + -2y = 1 + -1x Add '2y' to each side of the equation. kx + ky + -2y + 2y = 1 + -1x + 2y Combine like terms: -2y + 2y = 0 kx + ky + 0 = 1 + -1x + 2y kx + ky = 1 + -1x + 2y Reorder the terms: -1 + kx + ky + x + -2y = 1 + -1x + 2y + -1 + x + -2y Reorder the terms: -1 + kx + ky + x + -2y = 1 + -1 + -1x + x + 2y + -2y Combine like terms: 1 + -1 = 0 -1 + kx + ky + x + -2y = 0 + -1x + x + 2y + -2y -1 + kx + ky + x + -2y = -1x + x + 2y + -2y Combine like terms: -1x + x = 0 -1 + kx + ky + x + -2y = 0 + 2y + -2y -1 + kx + ky + x + -2y = 2y + -2y Combine like terms: 2y + -2y = 0 -1 + kx + ky + x + -2y = 0 The solution to this equation could not be determined.
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