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Simplifying 6x + 3yi = 3y + 6 + -3i Reorder the terms: 3iy + 6x = 3y + 6 + -3i Reorder the terms: 3iy + 6x = 6 + -3i + 3y Solving 3iy + 6x = 6 + -3i + 3y Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '3i' to each side of the equation. 3iy + 3i + 6x = 6 + -3i + 3i + 3y Reorder the terms: 3i + 3iy + 6x = 6 + -3i + 3i + 3y Combine like terms: -3i + 3i = 0 3i + 3iy + 6x = 6 + 0 + 3y 3i + 3iy + 6x = 6 + 3y Add '-6x' to each side of the equation. 3i + 3iy + 6x + -6x = 6 + -6x + 3y Combine like terms: 6x + -6x = 0 3i + 3iy + 0 = 6 + -6x + 3y 3i + 3iy = 6 + -6x + 3y Reorder the terms: -6 + 3i + 3iy + 6x + -3y = 6 + -6x + 3y + -6 + 6x + -3y Reorder the terms: -6 + 3i + 3iy + 6x + -3y = 6 + -6 + -6x + 6x + 3y + -3y Combine like terms: 6 + -6 = 0 -6 + 3i + 3iy + 6x + -3y = 0 + -6x + 6x + 3y + -3y -6 + 3i + 3iy + 6x + -3y = -6x + 6x + 3y + -3y Combine like terms: -6x + 6x = 0 -6 + 3i + 3iy + 6x + -3y = 0 + 3y + -3y -6 + 3i + 3iy + 6x + -3y = 3y + -3y Combine like terms: 3y + -3y = 0 -6 + 3i + 3iy + 6x + -3y = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + i + iy + 2x + -1y) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + i + iy + 2x + -1y)' equal to zero and attempt to solve: Simplifying -2 + i + iy + 2x + -1y = 0 Solving -2 + i + iy + 2x + -1y = 0 Move all terms containing i to the left, all other terms to the right. Add '2' to each side of the equation. -2 + i + iy + 2x + 2 + -1y = 0 + 2 Reorder the terms: -2 + 2 + i + iy + 2x + -1y = 0 + 2 Combine like terms: -2 + 2 = 0 0 + i + iy + 2x + -1y = 0 + 2 i + iy + 2x + -1y = 0 + 2 Combine like terms: 0 + 2 = 2 i + iy + 2x + -1y = 2 Add '-2x' to each side of the equation. i + iy + 2x + -2x + -1y = 2 + -2x Combine like terms: 2x + -2x = 0 i + iy + 0 + -1y = 2 + -2x i + iy + -1y = 2 + -2x Add 'y' to each side of the equation. i + iy + -1y + y = 2 + -2x + y Combine like terms: -1y + y = 0 i + iy + 0 = 2 + -2x + y i + iy = 2 + -2x + y 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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