If $x\left[\begin{array}{l}5 \\ 2\end{array}\right]+y\left[\begin{array}{l}-3 \\ -2\end{array}\right]=\left[\begin{array}{c}5 \\ -3\end{array}\right]$, then value of x and y will be

$\frac{19}{4}, \frac{25}{4}$

$x\begin{bmatrix}5\\2\end{bmatrix}+y\begin{bmatrix}-3\\-2\end{bmatrix}=\begin{bmatrix}5\\-3\end{bmatrix}.$

$5x-3y=5.$

$2x-2y=-3.$

$x-y=-\frac{3}{2}.$

$y=x+\frac{3}{2}.$

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

$2x-\frac{9}{2}=5.$

$2x=\frac{19}{2}.$

$x=\frac{19}{4}.$

$y=\frac{19}{4}+\frac{3}{2}=\frac{25}{4}.$

$x=\frac{19}{4},\;y=\frac{25}{4}.$