If$5x-8y=2,8x+5y=21$ , then $x,y$ are respectively.

$AX=B$

$X=A^{-1}B$

$\left[\begin{array}{c}x\\ y\end{array}\right]=\frac{1}{5\left(5\right)-\left(-8\right)\left(8\right)}\left[\begin{array}{cc}5& 8\\ -8& 5\end{array}\right]\left[\begin{array}{c}2\\ 21\end{array}\right]$

$=\frac{1}{89}\left[\begin{array}{c}5\left(2\right)+21\left(8\right)\\ -8\left(2\right)+5\left(21\right)\end{array}\right]$

$=\frac{1}{89}\left[\begin{array}{c}178\\ 89\end{array}\right]=\left[\begin{array}{c}\frac{178}{89}\\ \frac{89}{89}\end{array}\right]=\left[\begin{array}{c}2\\ 1\end{array}\right]$

$\therefore x=2,y=1$