解3元1次方程

x + y + z = 3 ......①
x - y + 3z = 7 .....②
2x + 3y - z = 0 ...③解法一(消去法) :
①×3 - ② :
3x + 3y + 3z - x + y - 3z = 9 - 7
2x + 4y = 2 .....④① + ③ :
3x + 4y = 3 .....⑤⑤ - ④ :
x = 1 , 代入④: 2 + 4y = 2,
y = 0 , 代 x = 1 , y = 0 入①: 1 + 0 + z = 3,
z = 2。解法二(代入法) :
由①, z = 3 - x - y , 分別代入②:
x - y + 3(3 - x - y) = 7
x - y + 9 - 3x - 3y = 7
2x + 4y - 2 = 0
x + 2y - 1 = 0 ......④及代入③:
2x + 3y - (3 - x - y) = 0
3x + 4y - 3 = 0 ....⑤由④, 2y = 1 - x , 代入⑤:
3x + 2(1 - x) - 3 = 0
x = 1 , 則2y = 1 - 1,
y = 0 ,
z = 3 - 1 - 0 = 2。