Solve system of equations with square roots and fractions $$
\begin{cases}
\left(\frac{1+\sqrt{3}}{2}\right)^2x+\left(\frac{1+\sqrt{3}}{2}\right)y+1=0\\
\left(\frac{1-\sqrt{3}}{2}\right)^2x+\left(\frac{1-\sqrt{3}}{2}\right)y+1=0
\end{cases}
$$
I tried setting the equations equal to each other and substituting variables but those methods just made the equation more conplicated. 

swetting $$a=\frac{1+\sqrt{3}}{2}$$ and $$b=\frac{1-\sqrt{3}}{2}$$ then we have to solve
$$a^2x+ay=-1$$
$$b^2x+by=-1$$
from the first equation we get
$$y=-\frac{1+a^2x}{a}$$
plugging this in the second equation we get
$$a^2bx-b(1+a^2x)=-1$$ thus
$$x=\frac{b-1}{ab^2-a^2b}$$
can you proceed?
