Question

HOTS Question:Solve: 2xy /x+y = 3/2, x+y≠0 and xy / 2x-y = -3 / 10, 2x-y≠0

Answer 1

$x = \frac{1}{2}$ and $y = - \frac{3}{2}$

Step-by-step explanation:

$\frac{2x}{x + y} = \frac{3}{2}$

$= > \frac{x + y}{xy} = \frac{4}{3}$

$= > \frac{1}{x} + \frac{1}{y} = \frac{4}{3}$---- Eq. 1

Then,

$\frac{xy}{2x - y} = - \frac{3}{10}$

$= > \frac{2x - y}{xy} = - \frac{10}{3}$

$= > - \frac{1}{x} + \frac{2}{y} = - \frac{10}{3}$-- Eq. 2

Let

$\frac{1}{x} = u$and

$\frac{1}{y} = v$.

Then, from Eq. 1 & 2, we get:

$u + v = \frac{4}{3}$ and

$- u + 2v = - \frac{10}{3}$

$= > 3u + 3v = 4$and

$- 3u + 6v= - 10$

By adding, we get,

$9v = - 6$

$= > v = \frac{ - 6}{9}$

$= > v = - \frac{2}{3}$

Substituting "y" got above in Eq.1, we get,

$\frac{1}{x} - \frac{2}{3} = \frac{4}{3}$

$= > \frac{1}{x} = \frac{6}{3} = 2$

$= > x = 2$

Hence,

$x = \frac{1}{2}$

$= > y = - \frac{3}{2}$