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Simplifying 2y + -6 + 4xi = 4x + -8 + -6yi Reorder the terms: -6 + 4ix + 2y = 4x + -8 + -6yi Reorder the terms: -6 + 4ix + 2y = -8 + -6iy + 4x Solving -6 + 4ix + 2y = -8 + -6iy + 4x Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '6iy' to each side of the equation. -6 + 4ix + 6iy + 2y = -8 + -6iy + 6iy + 4x Combine like terms: -6iy + 6iy = 0 -6 + 4ix + 6iy + 2y = -8 + 0 + 4x -6 + 4ix + 6iy + 2y = -8 + 4x Add '6' to each side of the equation. -6 + 4ix + 6iy + 6 + 2y = -8 + 6 + 4x Reorder the terms: -6 + 6 + 4ix + 6iy + 2y = -8 + 6 + 4x Combine like terms: -6 + 6 = 0 0 + 4ix + 6iy + 2y = -8 + 6 + 4x 4ix + 6iy + 2y = -8 + 6 + 4x Combine like terms: -8 + 6 = -2 4ix + 6iy + 2y = -2 + 4x Add '-2y' to each side of the equation. 4ix + 6iy + 2y + -2y = -2 + 4x + -2y Combine like terms: 2y + -2y = 0 4ix + 6iy + 0 = -2 + 4x + -2y 4ix + 6iy = -2 + 4x + -2y Reorder the terms: 2 + 4ix + 6iy + -4x + 2y = -2 + 4x + -2y + 2 + -4x + 2y Reorder the terms: 2 + 4ix + 6iy + -4x + 2y = -2 + 2 + 4x + -4x + -2y + 2y Combine like terms: -2 + 2 = 0 2 + 4ix + 6iy + -4x + 2y = 0 + 4x + -4x + -2y + 2y 2 + 4ix + 6iy + -4x + 2y = 4x + -4x + -2y + 2y Combine like terms: 4x + -4x = 0 2 + 4ix + 6iy + -4x + 2y = 0 + -2y + 2y 2 + 4ix + 6iy + -4x + 2y = -2y + 2y Combine like terms: -2y + 2y = 0 2 + 4ix + 6iy + -4x + 2y = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 2ix + 3iy + -2x + y) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 2ix + 3iy + -2x + y)' equal to zero and attempt to solve: Simplifying 1 + 2ix + 3iy + -2x + y = 0 Solving 1 + 2ix + 3iy + -2x + y = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 2ix + 3iy + -2x + -1 + y = 0 + -1 Reorder the terms: 1 + -1 + 2ix + 3iy + -2x + y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2ix + 3iy + -2x + y = 0 + -1 2ix + 3iy + -2x + y = 0 + -1 Combine like terms: 0 + -1 = -1 2ix + 3iy + -2x + y = -1 Add '2x' to each side of the equation. 2ix + 3iy + -2x + 2x + y = -1 + 2x Combine like terms: -2x + 2x = 0 2ix + 3iy + 0 + y = -1 + 2x 2ix + 3iy + y = -1 + 2x Add '-1y' to each side of the equation. 2ix + 3iy + y + -1y = -1 + 2x + -1y Combine like terms: y + -1y = 0 2ix + 3iy + 0 = -1 + 2x + -1y 2ix + 3iy = -1 + 2x + -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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