For what values of x and y are the following matrices equal?

$A=\begin{bmatrix}2x+1&3y\\0&y^2-5y\end{bmatrix},B=\begin{bmatrix}x+3&y^2+2\\0&-6\end{bmatrix}$.

(2, 2)

We have,

$\begin{bmatrix}2x+1&3y\\0&y^2-5y\end{bmatrix}=\begin{bmatrix}x+3&y^2+2\\0&-6\end{bmatrix}$

$⇒2x+1=x+3$        ..... (1)

$3y=y^2+2$          ..... (2)

$y^2−5y=−6$       ..... (3)

$⇒x=2$         [From Eq. (1)]

$y=1\, or\, 2$             [From Eq. (2)]

$y=2\, or\, 3$            [From Eq. (3)]

So, $x = 2, y = 2$