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Simplifying (1 + x + y) * dy = (1 + -6x + -7y) * dx Reorder the terms for easier multiplication: dy(1 + x + y) = (1 + -6x + -7y) * dx (1 * dy + x * dy + y * dy) = (1 + -6x + -7y) * dx Reorder the terms: (dxy + 1dy + dy2) = (1 + -6x + -7y) * dx (dxy + 1dy + dy2) = (1 + -6x + -7y) * dx Reorder the terms for easier multiplication: dxy + 1dy + dy2 = dx(1 + -6x + -7y) dxy + 1dy + dy2 = (1 * dx + -6x * dx + -7y * dx) Reorder the terms: dxy + 1dy + dy2 = (1dx + -7dxy + -6dx2) dxy + 1dy + dy2 = (1dx + -7dxy + -6dx2) Solving dxy + 1dy + dy2 = 1dx + -7dxy + -6dx2 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. dxy + 1dy + -1dx + dy2 = 1dx + -7dxy + -1dx + -6dx2 Reorder the terms: -1dx + dxy + 1dy + dy2 = 1dx + -7dxy + -1dx + -6dx2 Reorder the terms: -1dx + dxy + 1dy + dy2 = 1dx + -1dx + -7dxy + -6dx2 Combine like terms: 1dx + -1dx = 0 -1dx + dxy + 1dy + dy2 = 0 + -7dxy + -6dx2 -1dx + dxy + 1dy + dy2 = -7dxy + -6dx2 Add '7dxy' to each side of the equation. -1dx + dxy + 1dy + 7dxy + dy2 = -7dxy + 7dxy + -6dx2 Reorder the terms: -1dx + dxy + 7dxy + 1dy + dy2 = -7dxy + 7dxy + -6dx2 Combine like terms: dxy + 7dxy = 8dxy -1dx + 8dxy + 1dy + dy2 = -7dxy + 7dxy + -6dx2 Combine like terms: -7dxy + 7dxy = 0 -1dx + 8dxy + 1dy + dy2 = 0 + -6dx2 -1dx + 8dxy + 1dy + dy2 = -6dx2 Add '6dx2' to each side of the equation. -1dx + 8dxy + 1dy + 6dx2 + dy2 = -6dx2 + 6dx2 Reorder the terms: -1dx + 8dxy + 6dx2 + 1dy + dy2 = -6dx2 + 6dx2 Combine like terms: -6dx2 + 6dx2 = 0 -1dx + 8dxy + 6dx2 + 1dy + dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-1x + 8xy + 6x2 + y + 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 '(-1x + 8xy + 6x2 + y + y2)' equal to zero and attempt to solve: Simplifying -1x + 8xy + 6x2 + y + y2 = 0 Solving -1x + 8xy + 6x2 + y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + 8xy + 6x2 + y + x + y2 = 0 + x Reorder the terms: -1x + x + 8xy + 6x2 + y + y2 = 0 + x Combine like terms: -1x + x = 0 0 + 8xy + 6x2 + y + y2 = 0 + x 8xy + 6x2 + y + y2 = 0 + x Remove the zero: 8xy + 6x2 + y + y2 = x Add '-8xy' to each side of the equation. 8xy + 6x2 + y + -8xy + y2 = x + -8xy Reorder the terms: 8xy + -8xy + 6x2 + y + y2 = x + -8xy Combine like terms: 8xy + -8xy = 0 0 + 6x2 + y + y2 = x + -8xy 6x2 + y + y2 = x + -8xy Add '-6x2' to each side of the equation. 6x2 + y + -6x2 + y2 = x + -8xy + -6x2 Reorder the terms: 6x2 + -6x2 + y + y2 = x + -8xy + -6x2 Combine like terms: 6x2 + -6x2 = 0 0 + y + y2 = x + -8xy + -6x2 y + y2 = x + -8xy + -6x2 Add '-1y' to each side of the equation. y + -1y + y2 = x + -8xy + -6x2 + -1y Combine like terms: y + -1y = 0 0 + y2 = x + -8xy + -6x2 + -1y y2 = x + -8xy + -6x2 + -1y Add '-1y2' to each side of the equation. y2 + -1y2 = x + -8xy + -6x2 + -1y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = x + -8xy + -6x2 + -1y + -1y2 Simplifying 0 = x + -8xy + -6x2 + -1y + -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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