Exercise 9. Alexie and Baptiste each own a building. Each floor of Alexie's building has 3 bathrooms and 2 bedrooms. Baptiste, on the other hand, has 4 bathrooms and 3 bedrooms per floor. There are a total of 25 bathrooms and 18 bedrooms. Find the number of floors in Alexie's and Baptiste's buildings.

Only a numerical answer is expected here.
Solution to exercise 9 We let $a$ be the number of floors in Alexie's building and $b$ be the number of floors in Baptiste's building. The statement reduces to the following system of equations:

$$
\left\{\begin{array}{l}
3 a+4 b=25 \\
2 a+3 b=18
\end{array}\right.
$$

We multiply the first row by 2 and the second by 3 and we get

$$
\left\{\begin{array}{l}
6 a+8 b=50 \\
6 a+9 b=54
\end{array}\right.
$$

then we subtract to obtain

$$
b=4
$$

It is now sufficient to substitute back to get $6 a=50-32=18$ and thus

$$
a=3
$$

Alexie has a building with 3 floors and Baptiste has a building with 4 floors.