Solution (i) {x−2y+z=−13x+y−2z=4y−z=1\begin{cases} x-2y+z=-1\\ 3x+y-2z=4\\ y-z=1 \end{cases}⎩⎨⎧x−2y+z=−13x+y−2z=4y−z=1 Solution: x=1, y=1, z=0\boxed{x=1,\; y=1,\; z=0}x=1,y=1,z=0 (ii) {2x1+x2+3x3=3x1+3x2−2x3=0−3x1−x2+2x3=4\begin{cases} 2x_1+x_2+3x_3=3\\ x_1+3x_2-2x_3=0\\ -3x_1-x_2+2x_3=4 \end{cases}⎩⎨⎧2x1+x2+3x3=3x1+3x2−2x3=0−3x1−x2+2x3=4 Solution: x1=−89, x2=109, x3=119\boxed{x_1=-\frac{8}{9},\; x_2=\frac{10}{9},\; x_3=\frac{11}{9}}x1=−98,x2=910,x3=911 (iii) {x+y=22x−z=12y−3z=−1\begin{cases} x+y=2\\ 2x-z=1\\ 2y-3z=-1 \end{cases}⎩⎨⎧x+y=22x−z=12y−3z=−1 Solution: x=1, y=1, z=1\boxed{x=1,\; y=1,\; z=1}x=1,y=1,z=1