Finding the solution(s) for:
$$ \begin{align*} \begin{cases} 2x_1+x_2+3x_3+2x_4 &=5\\ x_1+x_2+x_3+2x_4&=3\\ -x_2+x_3+6x_4&=3 \end{cases} \end{align*} $$
I tried using elimination to rewrite the system in row echelon form, then back substituting. I have no idea what I did wrong, or if I was doing the elimination process correctly.. but I kept getting stuck. I am confused and not really sure how to proceed, I must be awful because I've been staring at this problem for hours.