If $x\left[\begin{array}{l}2\\ 1\end{array}\right]+y\left[\begin{array}{l}3\\ 5\end{array}\right]+\left[\begin{array}{l}-8\\ -11\end{array}\right]=0$ then  $(x,y)=\_\_\_$

$x\left[\begin{array}{l}2\\ 1\end{array}\right]+y\left[\begin{array}{l}3\\ 5\end{array}\right]+\left[\begin{array}{l}-8\\ -11\end{array}\right]=0$

$\Rightarrow \left[\begin{array}{l}2x+3y-8\\ 1x+5y-11\end{array}\right]=\left[\begin{array}{l}0\\ 0\end{array}\right]$

$\Rightarrow 2x+3y=8$

$x+5y=11$

Solve the above two equations.

$x=1,y=2$

$(x,y)=(1,2)$