Question

Giải hệ pt bằng phương pháp cộng đại số 

\(\left\{{}\begin{matrix}\sqrt{2x}-y=3\sqrt{2}\\x+\sqrt{2y}=3\end{matrix}\right.\)

Answer 1

\(\left\{{}\begin{matrix}\sqrt{2}x-y=3\sqrt{2}\\x+\sqrt{2}y=3\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}2x-y\sqrt{2}=6\\x+y\sqrt{2}=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-y\sqrt{2}+x+y\sqrt{2}=6+3\\x+y\sqrt{2}=3\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}3x=9\\y\sqrt{2}=3-x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y\sqrt{2}=3-3=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=3\\y=0\end{matrix}\right.\)