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Simplifying (3x + y) * dy + -1(x + 3y) * dx = 0 Reorder the terms for easier multiplication: dy(3x + y) + -1(x + 3y) * dx = 0 (3x * dy + y * dy) + -1(x + 3y) * dx = 0 (3dxy + dy2) + -1(x + 3y) * dx = 0 Reorder the terms for easier multiplication: 3dxy + dy2 + -1dx(x + 3y) = 0 3dxy + dy2 + (x * -1dx + 3y * -1dx) = 0 Reorder the terms: 3dxy + dy2 + (-3dxy + -1dx2) = 0 3dxy + dy2 + (-3dxy + -1dx2) = 0 Reorder the terms: 3dxy + -3dxy + -1dx2 + dy2 = 0 Combine like terms: 3dxy + -3dxy = 0 0 + -1dx2 + dy2 = 0 -1dx2 + dy2 = 0 Solving -1dx2 + dy2 = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'd'. d(-1x2 + y2) = 0 Factor a difference between two squares. d((x + y)(-1x + 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 '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-1x + y)' equal to zero and attempt to solve: Simplifying -1x + y = 0 Solving -1x + y = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + x + y = 0 + x Combine like terms: -1x + x = 0 0 + y = 0 + x y = 0 + x Remove the zero: y = x Add '-1y' to each side of the equation. y + -1y = x + -1y Combine like terms: y + -1y = 0 0 = x + -1y Simplifying 0 = x + -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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