Question

Tìm x,y, thuộc z biết a) (x-2) (y+1)=-1 b) (2x + 1) (y - 2)=3

Answer 1

a) Ta có: (x-2)(y+1)=-1

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-2=1\\y+1=-1\end{matrix}\right.\\\left\{{}\begin{matrix}x-2=-1\\y+1=1\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=3\\y=-2\end{matrix}\right.\\\left\{{}\begin{matrix}x=1\\y=0\end{matrix}\right.\end{matrix}\right.\)

Vậy: (x,y)={(3;-2);(1;0)}

b) Ta có: \(\left(2x+1\right)\left(y-2\right)=3\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2x+1=1\\y-2=3\end{matrix}\right.\\\left\{{}\begin{matrix}2x+1=3\\y-2=1\end{matrix}\right.\\\left\{{}\begin{matrix}2x+1=-1\\y-2=-3\end{matrix}\right.\\\left\{{}\begin{matrix}2x+1=-3\\y-2=-1\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2x=0\\y=5\end{matrix}\right.\\\left\{{}\begin{matrix}2x=2\\y=3\end{matrix}\right.\\\left\{{}\begin{matrix}2x=-2\\y=-1\end{matrix}\right.\\\left\{{}\begin{matrix}2x=-4\\y=1\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=0\\y=5\end{matrix}\right.\\\left\{{}\begin{matrix}x=1\\y=3\end{matrix}\right.\\\left\{{}\begin{matrix}x=-1\\y=-1\end{matrix}\right.\\\left\{{}\begin{matrix}x=-2\\y=1\end{matrix}\right.\end{matrix}\right.\)

Vậy: (x,y)={(0;5);(1;3);(-1;-1);(-2;1)}