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Simplifying (2 + k) * x + -1(1 + k) * y + -5 + -1k = 2x + y + -11 Reorder the terms for easier multiplication: x(2 + k) + -1(1 + k) * y + -5 + -1k = 2x + y + -11 (2 * x + k * x) + -1(1 + k) * y + -5 + -1k = 2x + y + -11 Reorder the terms: (kx + 2x) + -1(1 + k) * y + -5 + -1k = 2x + y + -11 (kx + 2x) + -1(1 + k) * y + -5 + -1k = 2x + y + -11 Reorder the terms for easier multiplication: kx + 2x + -1y(1 + k) + -5 + -1k = 2x + y + -11 kx + 2x + (1 * -1y + k * -1y) + -5 + -1k = 2x + y + -11 Reorder the terms: kx + 2x + (-1ky + -1y) + -5 + -1k = 2x + y + -11 kx + 2x + (-1ky + -1y) + -5 + -1k = 2x + y + -11 Reorder the terms: -5 + -1k + kx + -1ky + 2x + -1y = 2x + y + -11 Reorder the terms: -5 + -1k + kx + -1ky + 2x + -1y = -11 + 2x + y Add '-2x' to each side of the equation. -5 + -1k + kx + -1ky + 2x + -2x + -1y = -11 + 2x + -2x + y Combine like terms: 2x + -2x = 0 -5 + -1k + kx + -1ky + 0 + -1y = -11 + 2x + -2x + y -5 + -1k + kx + -1ky + -1y = -11 + 2x + -2x + y Combine like terms: 2x + -2x = 0 -5 + -1k + kx + -1ky + -1y = -11 + 0 + y -5 + -1k + kx + -1ky + -1y = -11 + y Solving -5 + -1k + kx + -1ky + -1y = -11 + y Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '5' to each side of the equation. -5 + -1k + kx + -1ky + 5 + -1y = -11 + 5 + y Reorder the terms: -5 + 5 + -1k + kx + -1ky + -1y = -11 + 5 + y Combine like terms: -5 + 5 = 0 0 + -1k + kx + -1ky + -1y = -11 + 5 + y -1k + kx + -1ky + -1y = -11 + 5 + y Combine like terms: -11 + 5 = -6 -1k + kx + -1ky + -1y = -6 + y Add 'y' to each side of the equation. -1k + kx + -1ky + -1y + y = -6 + y + y Combine like terms: -1y + y = 0 -1k + kx + -1ky + 0 = -6 + y + y -1k + kx + -1ky = -6 + y + y Combine like terms: y + y = 2y -1k + kx + -1ky = -6 + 2y Reorder the terms: 6 + -1k + kx + -1ky + -2y = -6 + 2y + 6 + -2y Reorder the terms: 6 + -1k + kx + -1ky + -2y = -6 + 6 + 2y + -2y Combine like terms: -6 + 6 = 0 6 + -1k + kx + -1ky + -2y = 0 + 2y + -2y 6 + -1k + kx + -1ky + -2y = 2y + -2y Combine like terms: 2y + -2y = 0 6 + -1k + kx + -1ky + -2y = 0 The solution to this equation could not be determined.
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