10.2 About numbers a and b, it is known that the system of equations

$$
\left\{\begin{array}{l}
y^{2}=x^{2}+a x+b \\
x^{2}=y^{2}+a y+b
\end{array}\right.
$$

has no solutions. Find a.
Solution: Since the system has no solutions, in particular, there are no solutions with $x=y$. When $x=y$, both equations of the system are equivalent to the equation $a x+b=0$. This linear equation has no roots only when its slope coefficient $a$ is zero.

## Criteria:

- Points are not deducted for the absence of an example of a system with $a=0$ that has no solutions.