Question

giải hệ pt sau bằng phương pháp thế

\(\left\{{}\begin{matrix}7\left|x+2\right|-2\left|y+1\right|=1\\3\left|x+2\right|+\left|y+1\right|=6\end{matrix}\right.\)

Answer 1

Đặt |x+2|=a

|y+1|=b

\(\Leftrightarrow\left\{{}\begin{matrix}7a-2b=1\\3a+b=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}7a-2b=1\\6a+2b=12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=1\\b=6-3a=3\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+2\in\left\{1;-1\right\}\\y+1\in\left\{3;-3\right\}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\in\left\{-1;-3\right\}\\y\in\left\{2;-4\right\}\end{matrix}\right.\)