Answer
$$x_1=0, \quad x_2=0 , \quad x_3=4, \quad x_4=-1, \quad x_5=2.$$
Work Step by Step
The augmented matrix is given by
$$
\left[ \begin {array}{cccccc} 1&5&3&0&0&14\\ 0&4&2&
5&0&3\\ 0&0&3&8&6&16\\ 2&4&0&0&-2&0
\\ 2&0&-1&0&0&0\end {array} \right]
.
$$
Using Gauss-Jordan elimination, we get the row-reduced echelon form as follows
$$\left[ \begin {array}{cccccc} 1&0&0&0&0&2\\ 0&1&0&0
&0&0\\ 0&0&1&0&0&4\\ 0&0&0&1&0&-1
\\ 0&0&0&0&1&2\end {array} \right]
.$$
From which we get the solution
$$x_1=0, \quad x_2=0 , \quad x_3=4, \quad x_4=-1, \quad x_5=2.$$
