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Simplifying (k + 2) * x + -1(k + 1) * y + 12 + -3k = 0 Reorder the terms: (2 + k) * x + -1(k + 1) * y + 12 + -3k = 0 Reorder the terms for easier multiplication: x(2 + k) + -1(k + 1) * y + 12 + -3k = 0 (2 * x + k * x) + -1(k + 1) * y + 12 + -3k = 0 Reorder the terms: (kx + 2x) + -1(k + 1) * y + 12 + -3k = 0 (kx + 2x) + -1(k + 1) * y + 12 + -3k = 0 Reorder the terms: kx + 2x + -1(1 + k) * y + 12 + -3k = 0 Reorder the terms for easier multiplication: kx + 2x + -1y(1 + k) + 12 + -3k = 0 kx + 2x + (1 * -1y + k * -1y) + 12 + -3k = 0 Reorder the terms: kx + 2x + (-1ky + -1y) + 12 + -3k = 0 kx + 2x + (-1ky + -1y) + 12 + -3k = 0 Reorder the terms: 12 + -3k + kx + -1ky + 2x + -1y = 0 Solving 12 + -3k + kx + -1ky + 2x + -1y = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -3k + kx + -1ky + 2x + -12 + -1y = 0 + -12 Reorder the terms: 12 + -12 + -3k + kx + -1ky + 2x + -1y = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -3k + kx + -1ky + 2x + -1y = 0 + -12 -3k + kx + -1ky + 2x + -1y = 0 + -12 Combine like terms: 0 + -12 = -12 -3k + kx + -1ky + 2x + -1y = -12 Add '-2x' to each side of the equation. -3k + kx + -1ky + 2x + -2x + -1y = -12 + -2x Combine like terms: 2x + -2x = 0 -3k + kx + -1ky + 0 + -1y = -12 + -2x -3k + kx + -1ky + -1y = -12 + -2x Add 'y' to each side of the equation. -3k + kx + -1ky + -1y + y = -12 + -2x + y Combine like terms: -1y + y = 0 -3k + kx + -1ky + 0 = -12 + -2x + y -3k + kx + -1ky = -12 + -2x + y Reorder the terms: 12 + -3k + kx + -1ky + 2x + -1y = -12 + -2x + y + 12 + 2x + -1y Reorder the terms: 12 + -3k + kx + -1ky + 2x + -1y = -12 + 12 + -2x + 2x + y + -1y Combine like terms: -12 + 12 = 0 12 + -3k + kx + -1ky + 2x + -1y = 0 + -2x + 2x + y + -1y 12 + -3k + kx + -1ky + 2x + -1y = -2x + 2x + y + -1y Combine like terms: -2x + 2x = 0 12 + -3k + kx + -1ky + 2x + -1y = 0 + y + -1y 12 + -3k + kx + -1ky + 2x + -1y = y + -1y Combine like terms: y + -1y = 0 12 + -3k + kx + -1ky + 2x + -1y = 0 The solution to this equation could not be determined.
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