Question

(x+y)÷xy=2 ; (x-y)÷xy=6 : solve using cross multiplication

Answer 1

x+yxy=2x+yxy=2          =>        1x+1y=21x+1y=2          =>       p+q=2p+q=2   .....(i)    [Let p=1x,q=1yp=1x,q=1y]

And           x−yxy=6x−yxy=6     =>        1x−1y=61x−1y=6          =>       p−q=6p−q=6   .....(ii)    [Let p=1x,q=1yp=1x,q=1y]

pb1c2−b2c1=qc1a2−c2a1=−1a1b2−a2b1pb1c2−b2c1=qc1a2−c2a1=−1a1b2−a2b1

=>     p1×6−(−1)×2=q2×1−6×1=−11×(−1)−1×1p1×6−(−1)×2=q2×1−6×1=−11×(−1)−1×1

=>     p8=q−4=−1−2p8=q−4=−1−2

Taking  p8=12p8=12        =>       p=4p=4

Taking q−4=12q−4=12      =>       q=−2q=−2

4=1x,−2=1y4=1x,−2=1y       =>       x=14,y=−12