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Simplifying (X + y)(dx + -1dy) = dy + dx Multiply (X + y) * (dx + -1dy) (X(dx + -1dy) + y(dx + -1dy)) = dy + dx ((dx * X + -1dy * X) + y(dx + -1dy)) = dy + dx ((dxX + -1dyX) + y(dx + -1dy)) = dy + dx (dxX + -1dyX + (dx * y + -1dy * y)) = dy + dx (dxX + -1dyX + (dxy + -1dy2)) = dy + dx Reorder the terms: (dxX + dxy + -1dyX + -1dy2) = dy + dx (dxX + dxy + -1dyX + -1dy2) = dy + dx Reorder the terms: dxX + dxy + -1dyX + -1dy2 = dx + dy Solving dxX + dxy + -1dyX + -1dy2 = dx + dy 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. dxX + dxy + -1dyX + -1dx + -1dy2 = dx + -1dx + dy Reorder the terms: -1dx + dxX + dxy + -1dyX + -1dy2 = dx + -1dx + dy Combine like terms: dx + -1dx = 0 -1dx + dxX + dxy + -1dyX + -1dy2 = 0 + dy -1dx + dxX + dxy + -1dyX + -1dy2 = dy Add '-1dy' to each side of the equation. -1dx + dxX + dxy + -1dyX + -1dy + -1dy2 = dy + -1dy Reorder the terms: -1dx + dxX + dxy + -1dy + -1dyX + -1dy2 = dy + -1dy Combine like terms: dy + -1dy = 0 -1dx + dxX + dxy + -1dy + -1dyX + -1dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-1x + xX + xy + -1y + -1yX + -1y2) = 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 + xX + xy + -1y + -1yX + -1y2)' equal to zero and attempt to solve: Simplifying -1x + xX + xy + -1y + -1yX + -1y2 = 0 Solving -1x + xX + xy + -1y + -1yX + -1y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + xX + xy + -1y + -1yX + x + -1y2 = 0 + x Reorder the terms: -1x + x + xX + xy + -1y + -1yX + -1y2 = 0 + x Combine like terms: -1x + x = 0 0 + xX + xy + -1y + -1yX + -1y2 = 0 + x xX + xy + -1y + -1yX + -1y2 = 0 + x Remove the zero: xX + xy + -1y + -1yX + -1y2 = x Add '-1xX' to each side of the equation. xX + xy + -1y + -1yX + -1xX + -1y2 = x + -1xX Reorder the terms: xX + -1xX + xy + -1y + -1yX + -1y2 = x + -1xX Combine like terms: xX + -1xX = 0 0 + xy + -1y + -1yX + -1y2 = x + -1xX xy + -1y + -1yX + -1y2 = x + -1xX Add '-1xy' to each side of the equation. xy + -1y + -1yX + -1xy + -1y2 = x + -1xX + -1xy Reorder the terms: xy + -1xy + -1y + -1yX + -1y2 = x + -1xX + -1xy Combine like terms: xy + -1xy = 0 0 + -1y + -1yX + -1y2 = x + -1xX + -1xy -1y + -1yX + -1y2 = x + -1xX + -1xy Add 'y' to each side of the equation. -1y + -1yX + y + -1y2 = x + -1xX + -1xy + y Reorder the terms: -1y + y + -1yX + -1y2 = x + -1xX + -1xy + y Combine like terms: -1y + y = 0 0 + -1yX + -1y2 = x + -1xX + -1xy + y -1yX + -1y2 = x + -1xX + -1xy + y Add 'yX' to each side of the equation. -1yX + yX + -1y2 = x + -1xX + -1xy + y + yX Combine like terms: -1yX + yX = 0 0 + -1y2 = x + -1xX + -1xy + y + yX -1y2 = x + -1xX + -1xy + y + yX Add 'y2' to each side of the equation. -1y2 + y2 = x + -1xX + -1xy + y + yX + y2 Combine like terms: -1y2 + y2 = 0 0 = x + -1xX + -1xy + y + yX + y2 Simplifying 0 = x + -1xX + -1xy + y + yX + y2 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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