Let 1/x = u and 1/y = v,
So the given equations becomes,
u/2 + v/3 = 2 ………………(i)
u/3 + v/2 = 13/6 ……………(ii)
From (i), we get
u/2 + v/3 = 2
⇒ 3u + 2v = 12
⇒ u = \(\frac{(12 – 2v)}{3}\) ………….(iii)
Using (iii) in (ii)
[(12 – 2v)/3]/3 + \(\frac{v}{2}\) = \(\frac{13}{6}\)
⇒ \(\frac{(12 – 2v)}{9 }\)+ v/2 = \(\frac{13}{6}\)
⇒ 24 – 4v + 9v = (\(\frac{13}{6}\)) x 18 [after taking LCM]
⇒ 24 + 5v = 39
⇒ 5v = 15
⇒ v = 3
Substituting v in (iii)
u = \(\frac{(12 – 2(3))}{3}\)
⇒ u = 2
Thus, x = \(\frac{1}{u}\)
⇒ x = \(\frac{1}{2}\) and y = \(\frac{1}{v}\)
⇒ y = \(\frac{1}{3}\)
The solution for the given pair of equations is x = \(\frac{1}{2}\) and y = \(\frac{1}{3}\) respectively.