## Task 1 - 291221

Determine all pairs $(x ; y)$ of real numbers $x, y$ that satisfy the following system of equations (1), (2), (3):

$$
\begin{aligned}
x + xy + xy^2 & = -21 \\
y + xy + x^2 y & = 14 \\
x + y & = -1
\end{aligned}
$$
Adding (1) and (2) results in the new equation

$$
(x+y)+2 x y+x y(x+y)=-7
$$

from which $x y=-6$ is immediately obtained using (3).

By substituting this into (1), one obtains the additional linear equation

$$
x-6 y=-15
$$

which, in conjunction with (3), ultimately leads to the unique solution $x=-3, y=2$.