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