34. Find all values of $a$ for which the system of equations

$$
\left\{\begin{array}{l}
x^{2}+y^{2}+2 x \leqslant 1 \\
x-y=-a
\end{array}\right. \text { has a unique solution. }
$$

Solve the inequalities given in № $35-41$.
34. Let's write down the equivalent system for the given one $\left\{\begin{array}{l}x+a=y \\ x^{2}+(x+a)^{2}+2 x \leqslant 1 .\end{array}\right.$

The unique solution will occur if the discriminant of the quadratic polynomial is zero, i.e., $(a+1)^{2}-2\left(a^{2}-1\right)=0$.

From this, $a=3, a=-1$.