(1-2i)x-13y=5x-(1+2i)y

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Solution for (1-2i)x-13y=5x-(1+2i)y equation:


Simplifying
(1 + -2i) * x + -13y = 5x + -1(1 + 2i) * y

Reorder the terms for easier multiplication:
x(1 + -2i) + -13y = 5x + -1(1 + 2i) * y
(1 * x + -2i * x) + -13y = 5x + -1(1 + 2i) * y

Reorder the terms:
(-2ix + 1x) + -13y = 5x + -1(1 + 2i) * y
(-2ix + 1x) + -13y = 5x + -1(1 + 2i) * y

Reorder the terms for easier multiplication:
-2ix + 1x + -13y = 5x + -1y(1 + 2i)
-2ix + 1x + -13y = 5x + (1 * -1y + 2i * -1y)

Reorder the terms:
-2ix + 1x + -13y = 5x + (-2iy + -1y)
-2ix + 1x + -13y = 5x + (-2iy + -1y)

Reorder the terms:
-2ix + 1x + -13y = -2iy + 5x + -1y

Solving
-2ix + 1x + -13y = -2iy + 5x + -1y

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '2iy' to each side of the equation.
-2ix + 1x + 2iy + -13y = -2iy + 5x + 2iy + -1y

Reorder the terms:
-2ix + 2iy + 1x + -13y = -2iy + 5x + 2iy + -1y

Reorder the terms:
-2ix + 2iy + 1x + -13y = -2iy + 2iy + 5x + -1y

Combine like terms: -2iy + 2iy = 0
-2ix + 2iy + 1x + -13y = 0 + 5x + -1y
-2ix + 2iy + 1x + -13y = 5x + -1y

Add '-1x' to each side of the equation.
-2ix + 2iy + 1x + -1x + -13y = 5x + -1x + -1y

Combine like terms: 1x + -1x = 0
-2ix + 2iy + 0 + -13y = 5x + -1x + -1y
-2ix + 2iy + -13y = 5x + -1x + -1y

Combine like terms: 5x + -1x = 4x
-2ix + 2iy + -13y = 4x + -1y

Add '13y' to each side of the equation.
-2ix + 2iy + -13y + 13y = 4x + -1y + 13y

Combine like terms: -13y + 13y = 0
-2ix + 2iy + 0 = 4x + -1y + 13y
-2ix + 2iy = 4x + -1y + 13y

Combine like terms: -1y + 13y = 12y
-2ix + 2iy = 4x + 12y

Reorder the terms:
-2ix + 2iy + -4x + -12y = 4x + -4x + 12y + -12y

Combine like terms: 4x + -4x = 0
-2ix + 2iy + -4x + -12y = 0 + 12y + -12y
-2ix + 2iy + -4x + -12y = 12y + -12y

Combine like terms: 12y + -12y = 0
-2ix + 2iy + -4x + -12y = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1ix + iy + -2x + -6y) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1ix + iy + -2x + -6y)' equal to zero and attempt to solve: Simplifying -1ix + iy + -2x + -6y = 0 Solving -1ix + iy + -2x + -6y = 0 Move all terms containing i to the left, all other terms to the right. Add '2x' to each side of the equation. -1ix + iy + -2x + 2x + -6y = 0 + 2x Combine like terms: -2x + 2x = 0 -1ix + iy + 0 + -6y = 0 + 2x -1ix + iy + -6y = 0 + 2x Remove the zero: -1ix + iy + -6y = 2x Add '6y' to each side of the equation. -1ix + iy + -6y + 6y = 2x + 6y Combine like terms: -6y + 6y = 0 -1ix + iy + 0 = 2x + 6y -1ix + iy = 2x + 6y 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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