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Simplifying (3x + -7y + 1) * dx + (3x + y + -7) * dy = 0 Reorder the terms: (1 + 3x + -7y) * dx + (3x + y + -7) * dy = 0 Reorder the terms for easier multiplication: dx(1 + 3x + -7y) + (3x + y + -7) * dy = 0 (1 * dx + 3x * dx + -7y * dx) + (3x + y + -7) * dy = 0 Reorder the terms: (1dx + -7dxy + 3dx2) + (3x + y + -7) * dy = 0 (1dx + -7dxy + 3dx2) + (3x + y + -7) * dy = 0 Reorder the terms: 1dx + -7dxy + 3dx2 + (-7 + 3x + y) * dy = 0 Reorder the terms for easier multiplication: 1dx + -7dxy + 3dx2 + dy(-7 + 3x + y) = 0 1dx + -7dxy + 3dx2 + (-7 * dy + 3x * dy + y * dy) = 0 Reorder the terms: 1dx + -7dxy + 3dx2 + (3dxy + -7dy + dy2) = 0 1dx + -7dxy + 3dx2 + (3dxy + -7dy + dy2) = 0 Reorder the terms: 1dx + -7dxy + 3dxy + 3dx2 + -7dy + dy2 = 0 Combine like terms: -7dxy + 3dxy = -4dxy 1dx + -4dxy + 3dx2 + -7dy + dy2 = 0 Solving 1dx + -4dxy + 3dx2 + -7dy + 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(x + -4xy + 3x2 + -7y + 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 '(x + -4xy + 3x2 + -7y + y2)' equal to zero and attempt to solve: Simplifying x + -4xy + 3x2 + -7y + y2 = 0 Solving x + -4xy + 3x2 + -7y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -4xy + 3x2 + -7y + -1x + y2 = 0 + -1x Reorder the terms: x + -1x + -4xy + 3x2 + -7y + y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + -4xy + 3x2 + -7y + y2 = 0 + -1x -4xy + 3x2 + -7y + y2 = 0 + -1x Remove the zero: -4xy + 3x2 + -7y + y2 = -1x Add '4xy' to each side of the equation. -4xy + 3x2 + -7y + 4xy + y2 = -1x + 4xy Reorder the terms: -4xy + 4xy + 3x2 + -7y + y2 = -1x + 4xy Combine like terms: -4xy + 4xy = 0 0 + 3x2 + -7y + y2 = -1x + 4xy 3x2 + -7y + y2 = -1x + 4xy Add '-3x2' to each side of the equation. 3x2 + -7y + -3x2 + y2 = -1x + 4xy + -3x2 Reorder the terms: 3x2 + -3x2 + -7y + y2 = -1x + 4xy + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 + -7y + y2 = -1x + 4xy + -3x2 -7y + y2 = -1x + 4xy + -3x2 Add '7y' to each side of the equation. -7y + 7y + y2 = -1x + 4xy + -3x2 + 7y Combine like terms: -7y + 7y = 0 0 + y2 = -1x + 4xy + -3x2 + 7y y2 = -1x + 4xy + -3x2 + 7y Add '-1y2' to each side of the equation. y2 + -1y2 = -1x + 4xy + -3x2 + 7y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1x + 4xy + -3x2 + 7y + -1y2 Simplifying 0 = -1x + 4xy + -3x2 + 7y + -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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