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Simplifying (2 + k) * x + -1(3 + -1k) * y + -4k + 14 = 0 Reorder the terms for easier multiplication: x(2 + k) + -1(3 + -1k) * y + -4k + 14 = 0 (2 * x + k * x) + -1(3 + -1k) * y + -4k + 14 = 0 Reorder the terms: (kx + 2x) + -1(3 + -1k) * y + -4k + 14 = 0 (kx + 2x) + -1(3 + -1k) * y + -4k + 14 = 0 Reorder the terms for easier multiplication: kx + 2x + -1y(3 + -1k) + -4k + 14 = 0 kx + 2x + (3 * -1y + -1k * -1y) + -4k + 14 = 0 Reorder the terms: kx + 2x + (1ky + -3y) + -4k + 14 = 0 kx + 2x + (1ky + -3y) + -4k + 14 = 0 Reorder the terms: 14 + -4k + kx + 1ky + 2x + -3y = 0 Solving 14 + -4k + kx + 1ky + 2x + -3y = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -4k + kx + 1ky + 2x + -14 + -3y = 0 + -14 Reorder the terms: 14 + -14 + -4k + kx + 1ky + 2x + -3y = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -4k + kx + 1ky + 2x + -3y = 0 + -14 -4k + kx + 1ky + 2x + -3y = 0 + -14 Combine like terms: 0 + -14 = -14 -4k + kx + 1ky + 2x + -3y = -14 Add '-2x' to each side of the equation. -4k + kx + 1ky + 2x + -2x + -3y = -14 + -2x Combine like terms: 2x + -2x = 0 -4k + kx + 1ky + 0 + -3y = -14 + -2x -4k + kx + 1ky + -3y = -14 + -2x Add '3y' to each side of the equation. -4k + kx + 1ky + -3y + 3y = -14 + -2x + 3y Combine like terms: -3y + 3y = 0 -4k + kx + 1ky + 0 = -14 + -2x + 3y -4k + kx + 1ky = -14 + -2x + 3y Reorder the terms: 14 + -4k + kx + 1ky + 2x + -3y = -14 + -2x + 3y + 14 + 2x + -3y Reorder the terms: 14 + -4k + kx + 1ky + 2x + -3y = -14 + 14 + -2x + 2x + 3y + -3y Combine like terms: -14 + 14 = 0 14 + -4k + kx + 1ky + 2x + -3y = 0 + -2x + 2x + 3y + -3y 14 + -4k + kx + 1ky + 2x + -3y = -2x + 2x + 3y + -3y Combine like terms: -2x + 2x = 0 14 + -4k + kx + 1ky + 2x + -3y = 0 + 3y + -3y 14 + -4k + kx + 1ky + 2x + -3y = 3y + -3y Combine like terms: 3y + -3y = 0 14 + -4k + kx + 1ky + 2x + -3y = 0 The solution to this equation could not be determined.
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