4. For what values of $a$ is the system $\left\{\begin{array}{l}3 x^{2}-x-a-10=0 \\ (a+4) x+a+12=0\end{array}\right.$ consistent? Solve the system for all permissible $a$.
Answer: 1) the system is consistent for $a=-10,-8,4$;

2) when $a=-8$, $x=1$; when $a=4$, $x=-2$; when $a=-10$, $x=\frac{1}{3}$.