Find $X$ and $Y$, if $2X+3Y=\begin{bmatrix} 2 & 3\\ 4 & 0\\ \end{bmatrix}$ and $3X+2Y=\begin{bmatrix} 2 & -2\\ -1 & 5\\ \end{bmatrix}$

$X=\begin{bmatrix} 2/5 & -12/5\\ -11/5 & 3\\ \end{bmatrix}$ and $Y=\begin{bmatrix} 4/5 & 1/5\\ 3/5 & 1\\ \end{bmatrix}$ $X=\begin{bmatrix} 2/5 & -12/5\\ -11/5 & 3\\ \end{bmatrix}$ and $Y=\begin{bmatrix} 2/5 & 13/5\\ 14/5 & -2\\ \end{bmatrix}$ $X=\begin{bmatrix} 12/5 & -12/5\\ 6/5 & 2\\ \end{bmatrix}$ and $Y=\begin{bmatrix} 8/5 & 1/5\\ 13/5 & 3\\ \end{bmatrix}$ $X=\begin{bmatrix} 2/5 & -12/5\\ -11/5 & 1\\ \end{bmatrix}$ and $Y=\begin{bmatrix} 14/5 & 1/5\\ 3/5 & 2\\ \end{bmatrix}$

$X=\begin{bmatrix} 2/5 & -12/5\\ -11/5 & 3\\ \end{bmatrix}$ and $Y=\begin{bmatrix} 2/5 & 13/5\\ 14/5 & -2\\ \end{bmatrix}$

Adding and subtracting the two given equations we get two equations $X+Y=\begin{bmatrix} 4/5 & 1/5\\ 3/5 & 1\\ \end{bmatrix}$ and $X-Y=\begin{bmatrix} 0 & -5\\ -5 & 5\\ \end{bmatrix}$. From here we can find $X$ and $Y$.