## Elementary Linear Algebra 7th Edition

$$x=2-3t, \quad y=6+5t , \quad z=t.$$
The augmented matrix is given by $$\left[ \begin {array}{cccc} 2&5&-19&34\\ 3&8&-31&54 \end {array} \right] .$$ Using Gauss-Jordan elimination, we get the row-reduced echelon form as follows $$\left[ \begin {array}{cccc} 1&0&3&2\\ 0&1&-5&6 \end {array} \right] .$$ Putting, $z=t$ and by the back substitution we get the solution $$x=2-3t, \quad y=6+5t , \quad z=t.$$