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Simplifying (2x + -2y + -1) * dy = (3x + -3y + 1) * dx Reorder the terms: (-1 + 2x + -2y) * dy = (3x + -3y + 1) * dx Reorder the terms for easier multiplication: dy(-1 + 2x + -2y) = (3x + -3y + 1) * dx (-1 * dy + 2x * dy + -2y * dy) = (3x + -3y + 1) * dx Reorder the terms: (2dxy + -1dy + -2dy2) = (3x + -3y + 1) * dx (2dxy + -1dy + -2dy2) = (3x + -3y + 1) * dx Reorder the terms: 2dxy + -1dy + -2dy2 = (1 + 3x + -3y) * dx Reorder the terms for easier multiplication: 2dxy + -1dy + -2dy2 = dx(1 + 3x + -3y) 2dxy + -1dy + -2dy2 = (1 * dx + 3x * dx + -3y * dx) Reorder the terms: 2dxy + -1dy + -2dy2 = (1dx + -3dxy + 3dx2) 2dxy + -1dy + -2dy2 = (1dx + -3dxy + 3dx2) Solving 2dxy + -1dy + -2dy2 = 1dx + -3dxy + 3dx2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dx' to each side of the equation. 2dxy + -1dy + -1dx + -2dy2 = 1dx + -3dxy + -1dx + 3dx2 Reorder the terms: -1dx + 2dxy + -1dy + -2dy2 = 1dx + -3dxy + -1dx + 3dx2 Reorder the terms: -1dx + 2dxy + -1dy + -2dy2 = 1dx + -1dx + -3dxy + 3dx2 Combine like terms: 1dx + -1dx = 0 -1dx + 2dxy + -1dy + -2dy2 = 0 + -3dxy + 3dx2 -1dx + 2dxy + -1dy + -2dy2 = -3dxy + 3dx2 Add '3dxy' to each side of the equation. -1dx + 2dxy + -1dy + 3dxy + -2dy2 = -3dxy + 3dxy + 3dx2 Reorder the terms: -1dx + 2dxy + 3dxy + -1dy + -2dy2 = -3dxy + 3dxy + 3dx2 Combine like terms: 2dxy + 3dxy = 5dxy -1dx + 5dxy + -1dy + -2dy2 = -3dxy + 3dxy + 3dx2 Combine like terms: -3dxy + 3dxy = 0 -1dx + 5dxy + -1dy + -2dy2 = 0 + 3dx2 -1dx + 5dxy + -1dy + -2dy2 = 3dx2 Add '-3dx2' to each side of the equation. -1dx + 5dxy + -1dy + -3dx2 + -2dy2 = 3dx2 + -3dx2 Reorder the terms: -1dx + 5dxy + -3dx2 + -1dy + -2dy2 = 3dx2 + -3dx2 Combine like terms: 3dx2 + -3dx2 = 0 -1dx + 5dxy + -3dx2 + -1dy + -2dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-1x + 5xy + -3x2 + -1y + -2y2) = 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 '(-1x + 5xy + -3x2 + -1y + -2y2)' equal to zero and attempt to solve: Simplifying -1x + 5xy + -3x2 + -1y + -2y2 = 0 Solving -1x + 5xy + -3x2 + -1y + -2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + 5xy + -3x2 + -1y + x + -2y2 = 0 + x Reorder the terms: -1x + x + 5xy + -3x2 + -1y + -2y2 = 0 + x Combine like terms: -1x + x = 0 0 + 5xy + -3x2 + -1y + -2y2 = 0 + x 5xy + -3x2 + -1y + -2y2 = 0 + x Remove the zero: 5xy + -3x2 + -1y + -2y2 = x Add '-5xy' to each side of the equation. 5xy + -3x2 + -1y + -5xy + -2y2 = x + -5xy Reorder the terms: 5xy + -5xy + -3x2 + -1y + -2y2 = x + -5xy Combine like terms: 5xy + -5xy = 0 0 + -3x2 + -1y + -2y2 = x + -5xy -3x2 + -1y + -2y2 = x + -5xy Add '3x2' to each side of the equation. -3x2 + -1y + 3x2 + -2y2 = x + -5xy + 3x2 Reorder the terms: -3x2 + 3x2 + -1y + -2y2 = x + -5xy + 3x2 Combine like terms: -3x2 + 3x2 = 0 0 + -1y + -2y2 = x + -5xy + 3x2 -1y + -2y2 = x + -5xy + 3x2 Add 'y' to each side of the equation. -1y + y + -2y2 = x + -5xy + 3x2 + y Combine like terms: -1y + y = 0 0 + -2y2 = x + -5xy + 3x2 + y -2y2 = x + -5xy + 3x2 + y Add '2y2' to each side of the equation. -2y2 + 2y2 = x + -5xy + 3x2 + y + 2y2 Combine like terms: -2y2 + 2y2 = 0 0 = x + -5xy + 3x2 + y + 2y2 Simplifying 0 = x + -5xy + 3x2 + y + 2y2 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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