Find the matrix $\mathrm{P}$ satisfying the matrix equation

$\left[\begin{array}{cc}2& 1\\ 3& 2\end{array}\right]\mathrm{P}\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]=\left[\begin{array}{cc}1& 2\\ 2& -1\end{array}\right]$.

Use matrix method to solve the following system of equations:

$5x+2y=4$

$7x+3y=5$.

Use matrix method to solve the following system of equations;

$4x-3y=3$

$3x-5y=7$.

Using matrix method, determine whether the following system of equations is consistent or inconsistent.

$x+2y=2$

$2x+3y=3$.

Using matrix method, determine whether the following system of equations is consistent or inconsistent.

$x+2y=9$

$2x+4y=7$.

Using matrix method, determine whether the following system of equations is consistent or inconsistent.

$3x-y+2z=3$

$2x+y+3z=5$

$x-2y-z=1$.

Using matrix method, determine whether the following system of equations is consistent or inconsistent.

$5x-y+4z=5$

$2x+3y+5z=2$

$5x-2y+6z=-1$.

solve the following system of equations by using matrix method:

$x+y=1$

$7x+7y=7$.

Using matrix method, solve the following system of equations:

$x-2y+3z=6$

$x+4y+z=12$

$x-3y+4z=1$.