2. If the real number $a$ ensures that for every real number $z$, the system of equations in $x$ and $y$
$$
\left\{\begin{array}{l}
x+a y=2 z, \\
x y=2 z^{2}+3 z+1
\end{array}\right.
$$

always has real solutions, then the range of values for $a$ is . $\qquad$
2. $-4 \leqslant a0$, and the discriminant of equation (2)
$$
\Delta_{2}=9 a^{2}+4 a(1-2 a)=a(a+4) \leqslant 0,
$$

i.e., $-4 \leqslant a \leqslant 0$.
Also, $a \neq 0$, so the range of values for $a$ is $-4 \leqslant a<0$.