Question

解方程组{4/x+y+6/x-y=3, 9/x-y-1/x+y=1

Answer 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