[ Systems of linear equations $]$ [ Methods for solving problems with parameters ]

For what values of $m$ do the equations $m x-1000=1001$ and $1001 x=m-1000 x$ have a common root?
The roots of these equations are the numbers ${ }^{2001 / m}$ and $m_{/ 2001}$, respectively. ${ }^{2001} / m=m / 2001 \Leftrightarrow m^{2}=2001^{2} \Leftrightarrow$ $m= \pm 2001$.

Answer

For $m= \pm 2001$.

## Problem