\(a,\left\{{}\begin{matrix}3x-2y=5\\x+2y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4-2y\\3.\left(4-2y\right)-2y=5\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=4-2y\\-8y=5-12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4-2y\\y=\dfrac{7}{8}\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=4-2.\dfrac{7}{8}\\y=\dfrac{7}{8}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{9}{4}\\y=\dfrac{7}{8}\end{matrix}\right.\)
b)
ĐKXĐ: \(x\ge-1;y\ge2\)
\(\left\{{}\begin{matrix}2\sqrt{x+1}-3\sqrt{y-2}=5\\4\sqrt{x+1}+\sqrt{y-2}=17\end{matrix}\right.\left(I\right)\\ Đặt:\left\{{}\begin{matrix}\sqrt{x+1}=a\\\sqrt{y-2}=b\end{matrix}\right.\\ \left(I\right)\Leftrightarrow\left\{{}\begin{matrix}2a-3b=5\\4a+b=17\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}b=17-4a\\2a-3.\left(17-4a\right)=5\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}b=17-4a\\14a=56\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}b=17-4a\\a=4\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}b=1\\a=4\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}\sqrt{x+1}=4\\\sqrt{y-2}=1\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=15\\y=3\end{matrix}\right.\)
