Consider the simultaneous equations
$$\begin{array} { r }
3 x ^ { 2 } + 2 x y = 4 \\
x + y = a
\end{array}$$
where $a$ is a real constant.
Find the complete set of values of $a$ for which the equations have two distinct real solutions for $x$.
A There are no values of $a$.
B $- 2 < a < 2$
C $- 1 < a < 1$
D $a = 0$
E $a < - 1$ or $a > 1$
F $a < - 2$ or $a > 2$
G All real values of $a$