解方程{x+y+z=6 3x-y+2z=12 x-y-3z=-4

x + y + z = 6 (1) 3x - y + 2z = 12 (2) x - y - 3z = -4 (3)(1) + (2)得： 4x + 3z = 18 (4)(1) + (3)得： 2x - 2z = 2 (5)(4) - (5)×2得 7z = 14 解得： z = 2 把z = 2代入（5）得： x = (2 + 2z)/2 = (2 + 2×2)/2 = 3 把 x = 3 z = 2代入（1）得： y = 6 - x - z = 6 - 3 - 2 = 1 所以原方程组的解是 x = 3 , y = 1, z = 2