# Problem 2.

Find all values of the real parameter $p$ for which the system of equations is solvable

$$
\left\{\begin{aligned}
2[x]+y & =3 / 2 \\
3[x]-2 y & =p
\end{aligned}\right.
$$

Here $[a]$ denotes the integer part of the number $a$.
# Solution.

Solving the system with respect to the unknowns $[x]$ and $y$, we find

$$
[x]=\frac{p+3}{7}, \quad y=\frac{9}{14}-\frac{2 p}{7}
$$

It remains to determine when the value $\frac{p+3}{7}$ is an integer.

Answer. $p=7 k-3, k \in \mathbb{Z}$.