Find the value of x and y that satisfy the equations $\begin{bmatrix}3&-2\\3&0\\2&4\end{bmatrix}\begin{bmatrix}y&y\\x&x\end{bmatrix}=\begin{bmatrix}3&3\\3y&3y\\10&10\end{bmatrix}$.

$(\frac{3}{2},2)$

Given, $\begin{bmatrix}3&-2\\3&0\\2&4\end{bmatrix}\begin{bmatrix}y&y\\x&x\end{bmatrix}=\begin{bmatrix}3&3\\3y&3y\\10&10\end{bmatrix}$

or $\begin{bmatrix}3y-2x&3y-2x\\3y&3y\\2y+4x&2y+4x\end{bmatrix}=\begin{bmatrix}3&3\\3y&3y\\10&10\end{bmatrix}$

Comparing elements we have

$3y-2x=3$   ...(1)

$2y+4x+10$   ...(2)

Solving (1) and (2), we get $x = 3/2, y = 2$