Math, asked by navo13, 1 year ago

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

Answers

Answered by chandan727299
182
I hope here is ur answer
it helps u

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chandan727299: thanks
navo13: oh one mistake is there
chandan727299: where is one mistake
navo13: u have skipped x in subtraction with 9
navo13: sorry sorry i understand it now
navo13: again thanks
chandan727299: ooohhhh thanks
chandan727299: im right ya wrong
navo13: right
chandan727299: ooo yaaa tx
Answered by aquialaska
110

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}

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