Question

解方程组:2/(x+y)+5/(x-y)=18 9/(x+y)-10/(y-x)=66

Answer 1

2/(x+y)+5/(x-y)=18

9/(x+y)-10/(y-x)=66

设x+y=a,x-y=b,原方程化为

2/a+5/b=18 -----1(1)

9/a+10/b=66 -------(2)

(2)-(1)*2 得5/a=30 所以a=1/6 ；代入(1)式得b =5/6

于是有

x+y=1/6

x-y=5/6

两式相加得2x=1,所以x=1/2,代入任一方程得y=-1/3

即原方程的角是

x=1/2

y=-1/3