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Simplifying (x + 1) * dy = -1(y + -2) * dx Reorder the terms: (1 + x) * dy = -1(y + -2) * dx Reorder the terms for easier multiplication: dy(1 + x) = -1(y + -2) * dx (1 * dy + x * dy) = -1(y + -2) * dx Reorder the terms: (dxy + 1dy) = -1(y + -2) * dx (dxy + 1dy) = -1(y + -2) * dx Reorder the terms: dxy + 1dy = -1(-2 + y) * dx Reorder the terms for easier multiplication: dxy + 1dy = -1dx(-2 + y) dxy + 1dy = (-2 * -1dx + y * -1dx) dxy + 1dy = (2dx + -1dxy) Solving dxy + 1dy = 2dx + -1dxy Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-2dx' to each side of the equation. dxy + -2dx + 1dy = 2dx + -2dx + -1dxy Reorder the terms: -2dx + dxy + 1dy = 2dx + -2dx + -1dxy Combine like terms: 2dx + -2dx = 0 -2dx + dxy + 1dy = 0 + -1dxy -2dx + dxy + 1dy = -1dxy Add 'dxy' to each side of the equation. -2dx + dxy + dxy + 1dy = -1dxy + dxy Combine like terms: dxy + dxy = 2dxy -2dx + 2dxy + 1dy = -1dxy + dxy Combine like terms: -1dxy + dxy = 0 -2dx + 2dxy + 1dy = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-2x + 2xy + y) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(-2x + 2xy + y)' equal to zero and attempt to solve: Simplifying -2x + 2xy + y = 0 Solving -2x + 2xy + y = 0 Move all terms containing d to the left, all other terms to the right. Add '2x' to each side of the equation. -2x + 2xy + 2x + y = 0 + 2x Reorder the terms: -2x + 2x + 2xy + y = 0 + 2x Combine like terms: -2x + 2x = 0 0 + 2xy + y = 0 + 2x 2xy + y = 0 + 2x Remove the zero: 2xy + y = 2x Add '-2xy' to each side of the equation. 2xy + -2xy + y = 2x + -2xy Combine like terms: 2xy + -2xy = 0 0 + y = 2x + -2xy y = 2x + -2xy Add '-1y' to each side of the equation. y + -1y = 2x + -2xy + -1y Combine like terms: y + -1y = 0 0 = 2x + -2xy + -1y Simplifying 0 = 2x + -2xy + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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