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Simplifying (X + y + 1) * dx + (3x + 3y + -1) * dy = 0 Reorder the terms: (1 + X + y) * dx + (3x + 3y + -1) * dy = 0 Reorder the terms for easier multiplication: dx(1 + X + y) + (3x + 3y + -1) * dy = 0 (1 * dx + X * dx + y * dx) + (3x + 3y + -1) * dy = 0 (1dx + dxX + dxy) + (3x + 3y + -1) * dy = 0 Reorder the terms: 1dx + dxX + dxy + (-1 + 3x + 3y) * dy = 0 Reorder the terms for easier multiplication: 1dx + dxX + dxy + dy(-1 + 3x + 3y) = 0 1dx + dxX + dxy + (-1 * dy + 3x * dy + 3y * dy) = 0 Reorder the terms: 1dx + dxX + dxy + (3dxy + -1dy + 3dy2) = 0 1dx + dxX + dxy + (3dxy + -1dy + 3dy2) = 0 Combine like terms: dxy + 3dxy = 4dxy 1dx + dxX + 4dxy + -1dy + 3dy2 = 0 Solving 1dx + dxX + 4dxy + -1dy + 3dy2 = 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(x + xX + 4xy + -1y + 3y2) = 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 + xX + 4xy + -1y + 3y2)' equal to zero and attempt to solve: Simplifying x + xX + 4xy + -1y + 3y2 = 0 Solving x + xX + 4xy + -1y + 3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + xX + 4xy + -1y + -1x + 3y2 = 0 + -1x Reorder the terms: x + -1x + xX + 4xy + -1y + 3y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + xX + 4xy + -1y + 3y2 = 0 + -1x xX + 4xy + -1y + 3y2 = 0 + -1x Remove the zero: xX + 4xy + -1y + 3y2 = -1x Add '-1xX' to each side of the equation. xX + 4xy + -1y + -1xX + 3y2 = -1x + -1xX Reorder the terms: xX + -1xX + 4xy + -1y + 3y2 = -1x + -1xX Combine like terms: xX + -1xX = 0 0 + 4xy + -1y + 3y2 = -1x + -1xX 4xy + -1y + 3y2 = -1x + -1xX Add '-4xy' to each side of the equation. 4xy + -1y + -4xy + 3y2 = -1x + -1xX + -4xy Reorder the terms: 4xy + -4xy + -1y + 3y2 = -1x + -1xX + -4xy Combine like terms: 4xy + -4xy = 0 0 + -1y + 3y2 = -1x + -1xX + -4xy -1y + 3y2 = -1x + -1xX + -4xy Add 'y' to each side of the equation. -1y + y + 3y2 = -1x + -1xX + -4xy + y Combine like terms: -1y + y = 0 0 + 3y2 = -1x + -1xX + -4xy + y 3y2 = -1x + -1xX + -4xy + y Add '-3y2' to each side of the equation. 3y2 + -3y2 = -1x + -1xX + -4xy + y + -3y2 Combine like terms: 3y2 + -3y2 = 0 0 = -1x + -1xX + -4xy + y + -3y2 Simplifying 0 = -1x + -1xX + -4xy + y + -3y2 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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