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Simplifying [4x + -3y + -18] * dy = [2y + -1x + 7] * dx Reorder the terms: [-18 + 4x + -3y] * dy = [2y + -1x + 7] * dx Reorder the terms for easier multiplication: dy[-18 + 4x + -3y] = [2y + -1x + 7] * dx [-18 * dy + 4x * dy + -3y * dy] = [2y + -1x + 7] * dx Reorder the terms: [4dxy + -18dy + -3dy2] = [2y + -1x + 7] * dx [4dxy + -18dy + -3dy2] = [2y + -1x + 7] * dx Reorder the terms: 4dxy + -18dy + -3dy2 = [7 + -1x + 2y] * dx Reorder the terms for easier multiplication: 4dxy + -18dy + -3dy2 = dx[7 + -1x + 2y] 4dxy + -18dy + -3dy2 = [7 * dx + -1x * dx + 2y * dx] Reorder the terms: 4dxy + -18dy + -3dy2 = [7dx + 2dxy + -1dx2] 4dxy + -18dy + -3dy2 = [7dx + 2dxy + -1dx2] Solving 4dxy + -18dy + -3dy2 = 7dx + 2dxy + -1dx2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-7dx' to each side of the equation. 4dxy + -18dy + -7dx + -3dy2 = 7dx + 2dxy + -7dx + -1dx2 Reorder the terms: -7dx + 4dxy + -18dy + -3dy2 = 7dx + 2dxy + -7dx + -1dx2 Reorder the terms: -7dx + 4dxy + -18dy + -3dy2 = 7dx + -7dx + 2dxy + -1dx2 Combine like terms: 7dx + -7dx = 0 -7dx + 4dxy + -18dy + -3dy2 = 0 + 2dxy + -1dx2 -7dx + 4dxy + -18dy + -3dy2 = 2dxy + -1dx2 Add '-2dxy' to each side of the equation. -7dx + 4dxy + -18dy + -2dxy + -3dy2 = 2dxy + -2dxy + -1dx2 Reorder the terms: -7dx + 4dxy + -2dxy + -18dy + -3dy2 = 2dxy + -2dxy + -1dx2 Combine like terms: 4dxy + -2dxy = 2dxy -7dx + 2dxy + -18dy + -3dy2 = 2dxy + -2dxy + -1dx2 Combine like terms: 2dxy + -2dxy = 0 -7dx + 2dxy + -18dy + -3dy2 = 0 + -1dx2 -7dx + 2dxy + -18dy + -3dy2 = -1dx2 Add 'dx2' to each side of the equation. -7dx + 2dxy + -18dy + dx2 + -3dy2 = -1dx2 + dx2 Reorder the terms: -7dx + 2dxy + dx2 + -18dy + -3dy2 = -1dx2 + dx2 Combine like terms: -1dx2 + dx2 = 0 -7dx + 2dxy + dx2 + -18dy + -3dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-7x + 2xy + x2 + -18y + -3y2) = 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 '(-7x + 2xy + x2 + -18y + -3y2)' equal to zero and attempt to solve: Simplifying -7x + 2xy + x2 + -18y + -3y2 = 0 Solving -7x + 2xy + x2 + -18y + -3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '7x' to each side of the equation. -7x + 2xy + x2 + -18y + 7x + -3y2 = 0 + 7x Reorder the terms: -7x + 7x + 2xy + x2 + -18y + -3y2 = 0 + 7x Combine like terms: -7x + 7x = 0 0 + 2xy + x2 + -18y + -3y2 = 0 + 7x 2xy + x2 + -18y + -3y2 = 0 + 7x Remove the zero: 2xy + x2 + -18y + -3y2 = 7x Add '-2xy' to each side of the equation. 2xy + x2 + -18y + -2xy + -3y2 = 7x + -2xy Reorder the terms: 2xy + -2xy + x2 + -18y + -3y2 = 7x + -2xy Combine like terms: 2xy + -2xy = 0 0 + x2 + -18y + -3y2 = 7x + -2xy x2 + -18y + -3y2 = 7x + -2xy Add '-1x2' to each side of the equation. x2 + -18y + -1x2 + -3y2 = 7x + -2xy + -1x2 Reorder the terms: x2 + -1x2 + -18y + -3y2 = 7x + -2xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -18y + -3y2 = 7x + -2xy + -1x2 -18y + -3y2 = 7x + -2xy + -1x2 Add '18y' to each side of the equation. -18y + 18y + -3y2 = 7x + -2xy + -1x2 + 18y Combine like terms: -18y + 18y = 0 0 + -3y2 = 7x + -2xy + -1x2 + 18y -3y2 = 7x + -2xy + -1x2 + 18y Add '3y2' to each side of the equation. -3y2 + 3y2 = 7x + -2xy + -1x2 + 18y + 3y2 Combine like terms: -3y2 + 3y2 = 0 0 = 7x + -2xy + -1x2 + 18y + 3y2 Simplifying 0 = 7x + -2xy + -1x2 + 18y + 3y2 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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