Solve the system of equations below using the inverse of a matrix. \begin{align*} x_1+x_2+3x_3+x_4&=5\\ -2x_1-x_2-4x_3-x_4&=-7\\ x_1+4x_2+10x_3+2x_4&=9\\ -2x_1-4x_3+5x_4&=9 \end{align*}