3x+2y-z=1,2x-y+2z=5,5x-2y+3z=13

问题描述:

3x+2y-z=1,2x-y+2z=5,5x-2y+3z=13

3x+2y-z=1 (1)
2x-y+2z=5 (2)
5x-2y+3z=13 (3)
(1)*2+(2):
6x+4y-2z+2x-y+2z=7
8x+3y=7 (4)
(1)*3+(3):
9x+6y-3z+5x-2y+3z=16
14x+4y=16
7x+2y=8 (5)
(5)*3-(4)*2:
21x+6y-16x-6y=24-14
5x=10
x=2
代入(4):
16+3y=7
y=-3
代入(1):
6-6-z=1
z=-1
所以:
x=2
y=-3
z=-1

3x+2y-z=1 ①2x-y+2z=5 ②5x-2y+3z=13 ③由③+①得:8x+2z=14 即4x+z=7 ④由①+②×2得:7x+3z=11 ⑤由④×3-⑤得:5x=10x=2把x=2代入④得:8+z=7z=-1把x=2,z=-1代入②得:4-y-2=5y=-3所以方程组的解为:x=2 y=-3 z=...