(2-i)x+(5+6i)y=1-3i

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Solution for (2-i)x+(5+6i)y=1-3i equation: 


Simplifying
(2 + -1i) * x + (5 + 6i) * y = 1 + -3i

Reorder the terms for easier multiplication:
x(2 + -1i) + (5 + 6i) * y = 1 + -3i
(2 * x + -1i * x) + (5 + 6i) * y = 1 + -3i

Reorder the terms:
(-1ix + 2x) + (5 + 6i) * y = 1 + -3i
(-1ix + 2x) + (5 + 6i) * y = 1 + -3i

Reorder the terms for easier multiplication:
-1ix + 2x + y(5 + 6i) = 1 + -3i
-1ix + 2x + (5 * y + 6i * y) = 1 + -3i

Reorder the terms:
-1ix + 2x + (6iy + 5y) = 1 + -3i
-1ix + 2x + (6iy + 5y) = 1 + -3i

Reorder the terms:
-1ix + 6iy + 2x + 5y = 1 + -3i

Solving
-1ix + 6iy + 2x + 5y = 1 + -3i

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.
-1ix + 6iy + 2x + 3i + 5y = 1 + -3i + 3i

Reorder the terms:
3i + -1ix + 6iy + 2x + 5y = 1 + -3i + 3i

Combine like terms: -3i + 3i = 0
3i + -1ix + 6iy + 2x + 5y = 1 + 0
3i + -1ix + 6iy + 2x + 5y = 1

Add '-2x' to each side of the equation.
3i + -1ix + 6iy + 2x + -2x + 5y = 1 + -2x

Combine like terms: 2x + -2x = 0
3i + -1ix + 6iy + 0 + 5y = 1 + -2x
3i + -1ix + 6iy + 5y = 1 + -2x

Add '-5y' to each side of the equation.
3i + -1ix + 6iy + 5y + -5y = 1 + -2x + -5y

Combine like terms: 5y + -5y = 0
3i + -1ix + 6iy + 0 = 1 + -2x + -5y
3i + -1ix + 6iy = 1 + -2x + -5y

Reorder the terms:
-1 + 3i + -1ix + 6iy + 2x + 5y = 1 + -2x + -5y + -1 + 2x + 5y

Reorder the terms:
-1 + 3i + -1ix + 6iy + 2x + 5y = 1 + -1 + -2x + 2x + -5y + 5y

Combine like terms: 1 + -1 = 0
-1 + 3i + -1ix + 6iy + 2x + 5y = 0 + -2x + 2x + -5y + 5y
-1 + 3i + -1ix + 6iy + 2x + 5y = -2x + 2x + -5y + 5y

Combine like terms: -2x + 2x = 0
-1 + 3i + -1ix + 6iy + 2x + 5y = 0 + -5y + 5y
-1 + 3i + -1ix + 6iy + 2x + 5y = -5y + 5y

Combine like terms: -5y + 5y = 0
-1 + 3i + -1ix + 6iy + 2x + 5y = 0

The solution to this equation could not be determined.

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