# Problem 2.

Solve the system of equations

$$
\begin{cases}2\left[x_{1}\right]+x_{2} & =3 / 2 \\ 3\left[x_{1}\right]-2 x_{2} & =4\end{cases}
$$

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

#
# Solution.

Solving the system with respect to the unknowns $\left[x_{1}\right]$ and $x_{2}$, we find

$$
\left[x_{1}\right]=\frac{4+3}{7}=1, \quad x_{2}=\frac{9-16}{14}=-\frac{1}{2}
$$

Therefore, $x_{1}$ can be any number whose integer part is 1.

Answer: $x_{1} \in[1 ; 2), x_{2}=-1 / 2$.