Determine x and y

First , bust it up into its real and imaginary components:

2i=yi-3xi   and   x = y       since x = y, sub this into the first equation

2i =xi-3xi

2i = -2xi

x = -1       so   since x=y     y = -1  

$x+2i - y = i y - i 3x\\ (3i +1) x + 2i =y(1+i) \\ y = \dfrac{(3i+1)x + 2i}{1+i}\\ y = \dfrac{(2+4i)x + (2+2i)}{2} = (1+2i)x+(1+i)$

Now if both x and y are real you can apply EP's answer.