If $A=\left[\begin{array}{ll}x & 3 \\ 2 & y\end{array}\right], B=\left[\begin{array}{cc}2 y & 1 \\ 3 & x\end{array}\right]$ and $A+2 B=\left[\begin{array}{cc}6 & 5 \\ 8 & -2\end{array}\right]$ then the value of (x, y) is:

$(-2,2)$

The correct answer is Option (1) - $(-2,2)$

$A+2 B=\left[\begin{array}{cc}x+4y & 5 \\ 8 & y+2x\end{array}\right]\left[\begin{array}{cc}6 & 5 \\ 8 & -2\end{array}\right]$

$x+4y=6$   ...(1)

$y+2x=-2$   ...(2)

eq. (1) × 2 - eq. (2)

$2x+8y-y-2x=12-2$

$7y=14⇒y=2$

from (1) $x=-2$

$(-2,2)$