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

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

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

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

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

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

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

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

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

Solving for variable 'i'.

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.