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Simplifying ydx = 2(x + y) * dy Reorder the terms for easier multiplication: dxy = 2dy(x + y) dxy = (x * 2dy + y * 2dy) dxy = (2dxy + 2dy2) Solving dxy = 2dxy + 2dy2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-2dxy' to each side of the equation. dxy + -2dxy = 2dxy + -2dxy + 2dy2 Combine like terms: dxy + -2dxy = -1dxy -1dxy = 2dxy + -2dxy + 2dy2 Combine like terms: 2dxy + -2dxy = 0 -1dxy = 0 + 2dy2 -1dxy = 2dy2 Add '-2dy2' to each side of the equation. -1dxy + -2dy2 = 2dy2 + -2dy2 Combine like terms: 2dy2 + -2dy2 = 0 -1dxy + -2dy2 = 0 Factor out the Greatest Common Factor (GCF), '-1dy'. -1dy(x + 2y) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(x + 2y)' equal to zero and attempt to solve: Simplifying x + 2y = 0 Solving x + 2y = 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 + 2y = 0 + -1x Combine like terms: x + -1x = 0 0 + 2y = 0 + -1x 2y = 0 + -1x Remove the zero: 2y = -1x Add '-2y' to each side of the equation. 2y + -2y = -1x + -2y Combine like terms: 2y + -2y = 0 0 = -1x + -2y Simplifying 0 = -1x + -2y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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