${x}_{1}-{s}_{3}+3{x}_{4}=9$

${x}_{2}+2{x}_{3}-5{x}_{4}=8$

$0=0$ The augmented matrix does not contain a row in which the only nonzero entry appears in the last column. Therefore, this system of equations must be consistent. Convert the augmented matrix into a system of equations. $x}_{1}=9+{x}_{3}-3{x}_{4$

$x}_{2}=8-2{x}_{3}+5{x}_{4$

${x}_{3},\mathfrak{e}e$

${x}_{4},\mathfrak{e}e$ Solve for the leading entry for each individual equation. Determine the free variables, if any. ${x}_{1}=9+s-3t$

${x}_{2}=8-2s+5t$

${x}_{3}=s$

${x}_{4}=t$ Parameterize the free variables. $x=\left[\begin{array}{c}9\\ 8\\ 0\\ 0\end{array}\right]+s\left[\begin{array}{c}1\\ -2\\ 1\\ 0\end{array}\right]+t\left[\begin{array}{c}-3\\ 5\\ 0\\ 1\end{array}\right]$ And write the solution in vector form.