If $\left[\begin{array}{cc}2 x+y & 4 x \\ 5 x-7 & 4 x\end{array}\right]=\left[\begin{array}{cc}7 & 7 y-13 \\ y & x+6\end{array}\right]$, then $4 x+5 y$ is equal to

23

The correct answer is Option (4) → 23

$\begin{bmatrix}2x+y & 4x \\ 5x-7 & 4x\end{bmatrix} = \begin{bmatrix}7 & 7y-13 \\ y & x+6\end{bmatrix}$

$2x+y=7 \;\;\; (1)$

$4x=7y-13 \;\;\; (2)$

$5x-7=y \;\;\; (3)$

$4x=x+6 \Rightarrow 3x=6 \Rightarrow x=2$

$y=5x-7=10-7=3$

$4x+5y=8+15=23$

The value of $4x+5y$ is $23$.