解方程组：{4/x+y+6/x-y=3 9/x-y-1/x+y=1}

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解方程组：{4/x+y+6/x-y=3 9/x-y-1/x+y=1}
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解方程组：{4/x+y+6/x-y=3 9/x-y-1/x+y=1}
解方程组：{4/x+y+6/x-y=3 9/x-y-1/x+y=1}

解方程组：{4/x+y+6/x-y=3 9/x-y-1/x+y=1}
{4/x+y+6/x-y=3
{9/x-y-1/x+y=1
令1/(x+y)=a,1/(x-y)=b
则原方程组为
{4a+6b=3
{-a+9b=1
解得
{a=1/2
{:b=1/6
所以{x+y=2
{x-y=6
解得
{x=4
{y=-2

设1/x+y=t 1/x-y=v
则4t+6v=3 9v-t=1
t=9v-1
4(9v-1)+6v=3
36v-4+6v=3
42v=7
v=1/6
t=1/2
1/x+y=1/2 1/x-y=1/6
x+y=2 x-y=6
2x=8
x=4
y=-2

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