If $\left[\begin{array}{cc}5 x+8 & 7 \\ y+3 & 10 x+12\end{array}\right]=\left[\begin{array}{cc}2 & 3 y+1 \\ 5 & 0\end{array}\right]$, then the value of $5 x+3 y$ is equal to:

0

The correct answer is Option (4) → 0

$\begin{bmatrix}5x+8&7\\y+3&10x+12\end{bmatrix}=\begin{bmatrix}2&3y+1\\5&0\end{bmatrix}.$

$5x+8=2.$

$y+3=5.$

$10x+12=0.$

$5x=-6 \Rightarrow x=-\frac{6}{5}.$

$y=2.$

$5x+3y=5\left(-\frac{6}{5}\right)+3(2)=-6+6=0.$