Answer
The solution set is
${({(\frac{t}{3}-\frac{2s}{3})} , {(\frac{t}{3}+\frac{s}{3})} , t,s) | t,s\in\Re)}$.
Work Step by Step
System
${x-y+w=0 }$
${ 3x-z+2w=0}$
${x-4y+z+2w=0}$
Start with the augmented matrix row echelon form (Gauss-Jordan) as shown in the image below.