Hệ phương trình sau có bao nhiêu nghiệm? \(\left\{ \begin{array}{l}{y^2} + \left| y \right| = 0\\{y^2} + {x^2} - 8x = 0\end{array} \right.\)

Ta có: \(\left\{ \begin{array}{l}{y^2} + \left| y \right| = 0\,\,\,\,\left( {\,1} \right)\\{y^2} + {x^2} - 8x = 0\,\,\,\,\,\,\left( 2 \right)\end{array} \right.\,\)

\(\begin{array}{l}\left( 1 \right) \Leftrightarrow {\left| y \right|^2} + \left| y \right| = 0\\ \Leftrightarrow \left| y \right|\left( {\left| y \right| + 1} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l}\left| y \right| = 0\\\left| y \right| + 1 = 0\,\,\left( {vo\,\,nghiem} \right)\end{array} \right. \Leftrightarrow y = 0\end{array}\)

\(\begin{array}{l} \Rightarrow \left( 2 \right) \Leftrightarrow {x^2} - 8x = 0\\ \Leftrightarrow x\left( {x - 8} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l}x = 0\\x - 8 = 0\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = 0\\x = 8\end{array} \right.\end{array}\)

Vậy hệ phương trình đã cho có hai nghiệm \(\left( {x;y} \right) = \left( {0;0} \right)\) hoặc \(\left( {x;y} \right) = \left( {8;0} \right)\).