$解: (1) 把 ① 分别代入 ②, ③, 并联立, 得 \\ \left\{\begin{array}{l}2 x+x+1+z=1, \\ x-2(x+1)+z=-6,\end{array}\right. \\整理, 得 \left\{\begin{array}{l}3 x+z=0, \\ -x+z=-4,\end{array}\right. 解得 \left\{\begin{array}{l}x=1, \\ z=-3 .\end{array}\right. \\ 把 x=1 代人①, 得 y=2 .\\所以原方程组的解为 \left\{\begin{array}{l}x=1, \\ y=2, \\ z=-3 .\end{array}\right. \\$ $解: (2) 由①可令 x=2 k, y=3 k, z=4 k , \\代入②, 得 2 k-3 k +4 k=6 , 解得 k=2 ,\\所以原方程组的解为 \left\{\begin{array}{l}x=4, \\ y=6, \\ z=8 .\end{array}\right. \\$ $解: (3) ② +③, 得 3 x=21 , 解得 x=7 , \\代入 ③, 得 z=-8 ;\\把 x=7 代人①, 得 y=0 ,\\所以原方程组的解为 \left\{\begin{array}{l}x=7, \\ y=0, \\ z=-8 .\end{array}\right. \\$ $解: (4) ①-③, 得 3 z=18, z=6 ; 把 z=6 代入②, \\得 y+6= 10, y=4 ; ①-②, 得 x=3 ,\\所以原方程组的解为 \left\{\begin{array}{l}x=3, \\ y=4, \\ z=6 .\end{array}\right. \\$ $解: (5)② + ③, 得 2 x+y=8 ,④\\由 ① ④ 联立, 得 \left\{\begin{array}{l}x-y=1, \\ 2 x+y=8,\end{array}\right. 解得 \left\{\begin{array}{l}x=3, \\ y=2,\end{array}\right. \\代入 ②, 得 3+6+z=10 , 解得 z=1 ,\\所以原方程组的解为 \left\{\begin{array}{l}x=3, \\ y=2, \\ z=1 .\end{array}\right. \\$ $解:(6) ② \times 2- ①, 得 x+3 z=8 , ④\\③ - ②, 得 x-z=4 ,⑤\\由④ ⑤ 联立, 得 \left\{\begin{array}{l}x+3 z=8, \\ x-z=4,\end{array}\right. 解得 \left\{\begin{array}{l}x=5, \\ z=1,\end{array}\right. \\代入 ③, 得 y=-2 ,\\所以原方程组的解为 \left\{\begin{array}{l}x=5, \\ y=-2, \\ z=1 .\end{array}\right. \\$
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