If $A=\begin{bmatrix} 2x+y & -3\\4 & 2\end{bmatrix} $ and $B=\begin{bmatrix} 5 & 3x-2y \\2 & 1\end{bmatrix}$ are such that $A+B=\begin{bmatrix} 0 & 0\\6 & 3\end{bmatrix}$ then values of x and y are respectively :

-1, -3

The correct answer is Option (4) → -1, -3

$A+B=\begin{bmatrix} 2x+y+5 & 3x-2y-3\\6 & 3\end{bmatrix}=\begin{bmatrix}0&0\\6&3\end{bmatrix}$

so $2x+y=-5$ ...(1)

$3x-2y=3$  ...(2)

2 × eq. 1 + eq. 2

$4x+2y+3x-2y=-10+3$

$7x=-7⇒x=-1$

from (1) $-2+y=-5$

$⇒y=-3$