Question

2x+2y+10z=100 7x+4y=200 17x+7y+30z=400 求怎么解

Answer 1

2x+2y+10z=100 ..............1
x+4y=200 ..............2
17x+7y+30z=400................3

由1式得
x+y+5z=50..............4
3式-4式*6得
11x+y=100.................5
5式*4-2式得
43x=200
x=200/43
将x=200/43代入2式得
200/43+4y=200
4y=8600/43-200/43
4y=8400/43
y=2100/43
将x=200/43,y=2100/43代入4式得

200/43+2100/43+5z=50
2300/43+5z=50
460/43+z=10
z=-30/43

所以x=200/43,y=2100/43,z=-30/43

Answer 2

2x+2y+10z=100…………①
7x+4y=200…………②
17x+7y+30z=400…………③
③-①x3得
11x+y=100…………④
④x4-②得
37x=200
x=200/37
将x=200/37代入②得
1400/37+4y=200
4y=6000/37
y=1500/37
将x=200/37，y=1500/37代入①得
400/37+3000/37+10z=100
3400/37+10z=100
10z=300/37
z=30/37
∴x=200/37，y=1500/37，z=30/37

Answer 3

2x+2y+10z=100 (1)
7x+4y=200 (2)
17x+7y+30z=400 (3)

(3)-(1)×3
11x+y=100 (4(
(4)×4-(2)
37x=200
所以x=200/37
y=100-11x=1500/37
z=(100-2x-2y)/10=30/37