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Simplifying (x + 3y) * dy + -1(3x + y) * dy = 0 Reorder the terms for easier multiplication: dy(x + 3y) + -1(3x + y) * dy = 0 (x * dy + 3y * dy) + -1(3x + y) * dy = 0 (dxy + 3dy2) + -1(3x + y) * dy = 0 Reorder the terms for easier multiplication: dxy + 3dy2 + -1dy(3x + y) = 0 dxy + 3dy2 + (3x * -1dy + y * -1dy) = 0 dxy + 3dy2 + (-3dxy + -1dy2) = 0 Reorder the terms: dxy + -3dxy + 3dy2 + -1dy2 = 0 Combine like terms: dxy + -3dxy = -2dxy -2dxy + 3dy2 + -1dy2 = 0 Combine like terms: 3dy2 + -1dy2 = 2dy2 -2dxy + 2dy2 = 0 Solving -2dxy + 2dy2 = 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), '2dy'. 2dy(-1x + y) = 0 Ignore the factor 2.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 '(-1x + y)' equal to zero and attempt to solve: Simplifying -1x + y = 0 Solving -1x + y = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + x + y = 0 + x Combine like terms: -1x + x = 0 0 + y = 0 + x y = 0 + x Remove the zero: y = x Add '-1y' to each side of the equation. y + -1y = x + -1y Combine like terms: y + -1y = 0 0 = x + -1y Simplifying 0 = x + -1y 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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