Question

2xy/x+y=3/2 and xy/2x-y=-3/10

Answer 1

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Answer 2

Answer:

Solution of given system of equation is $x=\frac{1}{2}\:\:and\:\:y=\frac{-3}{2}$

Step-by-step explanation:

Given system of equations are $\frac{2xy}{x+y}=\frac{3}{2}\:\:and\:\:\frac{xy}{2x-y}=\frac{-3}{10}$

Rewrite the equation by doing reciprocal on both sides of both equations.

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

$\frac{1}{2y}+\frac{1}{2x}=\frac{2}{3}\:\:and\:\:\frac{2}{y}-\frac{1}{x}=\frac{-10}{3}$

let  $\frac{1}{x}=u\:\:and\:\:\frac{1}{y}=v$

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

$v+u=\frac{4}{3}\:\:and\:\:2v-u=\frac{-10}{3}$

$3v+3u=4$..............(1)

$6v-3u=-10$............(2)

We solve it by Elimination  Method,

add (1) and (2)

9v = -6 ⇒ $v=\frac{-2}{3}$

Put this in equation (1)

$3\times\frac{-2}{3}+3u=4$

$-2+3u=4$

$3u=6$

$u=2$

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

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

Therefore, Solution of given system of equation is $x=\frac{1}{2}\:\:and\:\:y=\frac{-3}{2}$