Solve the following system of equations:1/(2x) + 1/(3y) = 2; 1/(3x) +

1.	Solve the following system of equations:1/(2x) + 1/(3y) = 2; 1/(3x) + 1/(2y) = 13/6
Answer» 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.

Solve the following system of equations:1/(2x) + 1/(3y) = 2; 1/(3x) + 1/(2y) = 13/6

Answer»

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.