JEE Math Practice Question

Let for some real numbers $$\alpha$$ and $$\beta$$, $$a = \alpha - i\beta $$. If the system of equations $$4ix + (1 + i)y = 0$$ and $$8\left( {\cos {{2\pi } \over 3} + i\sin {{2\pi } \over 3}} \right)x + \overline a y = 0$$ has more than one solution, then $${\alpha \over \beta }$$ is equal to

1. A.$$ - 2\sqrt 3 $$
2. B.$$2 - \sqrt 3 $$
3. C.$$2 + \sqrt 3 $$
4. D.$$ - 2 - \sqrt 3 $$