Bài giải:

x² + y² + 2x + 1 = 0

$\Leftrightarrow $ x² + 2x + 1 + y² = 0

$\Leftrightarrow $(x + 1)² + y² = 0

$\Leftrightarrow $$\left\{ \begin{align}& {{(x+1)}^{2}}=0 \\ & {{y}^{2}}=0 \\\end{align} \right.$                        

$\Leftrightarrow \left\{ \begin{align}& x+1=0 \\ & y=0 \\ \end{align} \right.$                                 

$\Leftrightarrow \left\{ \begin{align}& x=-1 \\ & y=0 \\ \end{align} \right.$

Vậy: (x; y) = (-1; 0).