Q:

Help solving system of equations

I've been trying to solve this problem for a good 2 hours and I still couldn't find the solution please help. 
$$
\left\{ 
\begin{array}{c}
4x^2-3xy-y^2=0 \\ 
32x^2-36xy+9y^2=6 \\ 
\end{array}
\right.  
$$

A:

From the first equation, you get
$$\begin{equation}\begin{aligned}
4x^2 - 3xy - y^2 & = 0 \\
(4x + y)(x - y) & = 0
\end{aligned}\end{equation}\tag{1}\label{eq1A}$$
which gives that
$$y = -4x \; \text{ or } \; y = x \tag{2}\label{eq2A}$$
Substitute these $2$ possibilities into the second equation & simplify the results.  Do you think you can finish the rest?