Question

a) \(\left\{{}\begin{matrix}2\sqrt{2x+3y}+\sqrt{5-x-y}=7\\3\sqrt{5-x-y}-\sqrt{2x+y-3}=1\end{matrix}\right.\)

b) \(\left\{{}\begin{matrix}\sqrt{8y-x}+x=2\\\sqrt{3y-x}+x+y=2\end{matrix}\right.\)

Answer 1

\(a,\left\{{}\begin{matrix}2\sqrt{2x+3y}+\sqrt{5-x-y}=7\\3\sqrt{5-x-y}-\sqrt{2x+y-3}=1\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}6\sqrt{2x+3y}+3\sqrt{5x-y}=21\\3\sqrt{5-x-y}-\sqrt{2x+3y}=1\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}7\sqrt{2x+3y}=21\\\sqrt{2x+3y}=3\end{matrix}\right.\)

Thay vào \(\rightarrow\sqrt{5-x-y}=1\)

\(\Rightarrow\left\{{}\begin{matrix}2x+3y=9\\5-x-y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+3y=9\\x+y=4\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=1\\y=3\end{matrix}\right.\)

Answer 2