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令a=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

解方程组{4/x+y+6/x-y=3, 9/x-y-1/x+y=1
令a=1/(x+y),b=1/(x-y)
4a+6b=3 (1)
9b-a=1 (2)
(1)+(2)×4
6b+36b=3+4
42b=7
b=1/6
a=9b-1=1/2
所以
x+y=1/a=2
x-y=1/b=6
相加
2x=8
x=4
y=x-6=-2

设1/x+y=a; 1/x-y=b;
则方程组变为:
4a +6b=3;
9b-a =1;
b=1/6;
a=1/2;
即: 1/x+y= 1/2 ; 1/x-y= 1/6;
所以有:
x+y=2; (1)
x-y=6;(2)
解方程组:得, x =4,y=-2;

LZ是不是抄错了,这组方程组里面的Y可以取任何值嘛,本人高三ing,仅能用高中知识想,有错请指导...

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