If $\begin{bmatrix} 2x + y & 4x \\ 5x - 7 & 4x \end{bmatrix} = \begin{bmatrix} 7 & 7y - 13 \\ y & x + 6 \end{bmatrix}$, then the value of $x + y$ is

5

The correct answer is Option (2) → 5 ##

Since, both the matrices are equal.

$∴$ On comparing the corresponding elements of both sides, we get

$4x = x + 6 \Rightarrow x = 2 \quad \dots(i)$

and $4x = 7y - 13 \Rightarrow 8 = 7y - 13 \quad [∵x = 2 \text{ from Eq. (i)}]$

$\Rightarrow 7y = 21 \Rightarrow y = 3$

$∴x + y = 2 + 3 = 5$