三元一次方程组： 2x-y+8z=3 ............ (1) 3x+4y-8z=8 ........... (2) x+y-2z=-3 ............ (3) 消去z：(1)+(2): 5x+3y=11 ............ (4) (1)+(3)*4: 6x+3y=-9 ............ (5) 消去y：(1)+(3): 3x+6z=0 ............. (4) (2)+(1)*4: 11x+24z=20 .......... (5) 消去x：(3)*2-(1): 3y-12z=-9 ........... (4) (2)-(3)*3: y-2z=17 ............. (5) 一般地，三元一次方程组： a1x+b1y+c1z=d1 ............ (1) a2x+b2y+c2z=d2 ............ (2) a3x+b3y+c3z=d3 ............ (3) 消去z：(1)*c2-(2)*c1: (a1c2-a2c1)x+(b1c2-b2c1)y=d1c2-d2c1 (2)*c3-(3)*c2: (a2c3-a3c2)x+(b2c3-b3c2)y=d2c3-d3c2 消去y：(1)*b2-(2)*b1: (a1b2-a2b1)x+(c1b2-c2b1)y=d1b2-d2b1 (2)*b3-(3)*b2: (a2b3-a3b2)x+(c2b3-c3b2)y=d2b3-d3b2 消去x：(1)*a2-(2)*a1: (b1a2-b2a1)x+(c1a2-c2a1)y=d1a2-d2a1 (2)*a3-(3)*a2: (b2a3-b3a2)x+(c2a3-c3a2)y=d2a3-d3a2
