Question

解方程组x/a+y/b=1,x/b+y/a=1那种方法简便

Answer 1

x/a+y/b=1............1
x/b+y/a=1...................2
1式+2式得
x(1/a+1/b)+y(1/a+1/b)=2
x+y=2/(1/a+1/b).........................3
1式-2式得
x(1/a-1/b)+y(1/b-1/a)=0
x(1/a-1/b)-y(1/a-1/b)=0
x-y=0
x=y........................4
将4式代入3式
2x=2/(1/a+1/b)
x=1/(1/a+1/b)
x=1/[(a+b)/ab]
x=ab/(a+b)

所以x=y=ab/(a+b)