Question

Solve for x and y:

$\frac{1}{2x}+\frac{1}{3y}=2,\frac{1}{3x}+\frac{1}{2y}=\frac{13}{6}(x\ne 0,y\ne 0).$

Answer 1

1/2x+1/3y=2,

1/3x+1/2y=13/6

Let 1/x =u

Let 1/y =v

u/2+v/3=2

(3u+2v)/6=2

3u+2v=12 ……….(i)

And,
u/3+v/2= 13/6
(2u+3v)/6=13/6
2u+3v=13........(ii)
from (i) and (ii)

v=3 and u=2

1/u =x = 1/2

1/v =y = 1/3