The system can be written in Matrix form as

So as a matrix equation this gives

From here try to Diagonalize the matrix, if that is not possible use the Jordan canonical form. So now we have a matrix that gives

So make the substitution

This gives

and now multiply by P to get

If the matrix was diagonalizable, this will uncouple the linear system into two ODEs. If you could only find JCF then the system will look like

So you have solve for and sub that into the first equation