Find the vector form of the solutions to the system of equations below. \begin{align*} 2x_1-4x_2+3x_3+x_5&=6\\ x_1-2x_2-2x_3+14x_4-4x_5&=15\\ x_1-2x_2+x_3+2x_4+x_5&=-1\\ -2x_1+4x_2-12x_4+x_5&=-7 \end{align*}