Question

solve x&y, xy\x+y=1/5, xy\x-y=1/7,

Answer 1

Reciprocal both eq
x/xy+y/xy=5
1/y+1/x=5.....1
x/xy-y/xy=7
1/y-1/x=7...2
Adding 1 and 2
We get 2/y=12
1/y=6...3
==>y=1/6
Putting 3 in 1
1/x+6=5
1/x=-1x=-1

Answer 2

given xy/x+y=1/5,xy/x-y=1/7.
take,xy/x+y=1/5.
Multiply LHS with x-y on both numerator and denominator.
xy/x+y*x+y/x-y=1/5
x²+xy+yx+y²/(x²-y²)=1/5
x²+2xy+y²=x²-y²/5
(x+y)²/5=x²-y²
1/5=x²-y²/(x+y)(x+y)
1/5=-y²/2y
2y=-5y²
2=-5y
y=2/-5.
x=substitute the y value in the equation to get x.