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Simplifying x + [k + 1] * y + 1 = 0 Reorder the terms: x + [1 + k] * y + 1 = 0 Reorder the terms for easier multiplication: x + y[1 + k] + 1 = 0 x + [1 * y + k * y] + 1 = 0 Reorder the terms: x + [ky + 1y] + 1 = 0 x + [ky + 1y] + 1 = 0 Reorder the terms: 1 + ky + x + 1y = 0 Solving 1 + ky + x + 1y = 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 + ky + x + -1 + 1y = 0 + -1 Reorder the terms: 1 + -1 + ky + x + 1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + ky + x + 1y = 0 + -1 ky + x + 1y = 0 + -1 Combine like terms: 0 + -1 = -1 ky + x + 1y = -1 Add '-1x' to each side of the equation. ky + x + -1x + 1y = -1 + -1x Combine like terms: x + -1x = 0 ky + 0 + 1y = -1 + -1x ky + 1y = -1 + -1x Add '-1y' to each side of the equation. ky + 1y + -1y = -1 + -1x + -1y Combine like terms: 1y + -1y = 0 ky + 0 = -1 + -1x + -1y ky = -1 + -1x + -1y Divide each side by 'y'. k = -1y-1 + -1xy-1 + -1 Simplifying k = -1y-1 + -1xy-1 + -1 Reorder the terms: k = -1 + -1xy-1 + -1y-1
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