求解二元一次方程组120/(x+y) + 80/(x-y)=1630/(x+y) + 60/(x-y)=8120/(x+y) + 80/(x-y)=1630/(x+y) + 60/(x-y)=8

问题描述:

求解二元一次方程组120/(x+y) + 80/(x-y)=1630/(x+y) + 60/(x-y)=8
120/(x+y) + 80/(x-y)=16
30/(x+y) + 60/(x-y)=8

设1/(x+y)=a,1/(x-y)=b
120a+80b=16
30a+60b=8
得a=1/15,b=1/10
则:x+y=15
x-y=10
的:x=12.5,y=2.5

令a=1/(x+y)
b=1/(x-y)
15a+10b=2 (1)
15a+30b=4 (2)
相减
20b=2
b=1/10
a=(2-10b)/15=1/15
所以
x+y=1/a=15
x-y=1/b=10
相加
2x=25
所以
x=25/2
y=15-x=5/2