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2/x +3/y =9/xy

4/x +9/y = 21/xy

Hi!
Here is the answer to your question.
 
The given system of equation is

When x = 1, we get
3 × 1 + 2y = 9  ( Using (1))
⇒ 3 + 2y = 9
⇒ 2y = 9 – 3 = 6

Thus, the solution of the given equations is x = 1 and y = 3.

Cheers!

  • 12
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 ok see here :

2/x + 3/y = 9/xy 

(2y+3x)/xy = 9/xy

2y + 3x = 9/xy    * xy

2y+3x=9

now in second equation 

4/x   +  9/y = 21/xy

(4y + 9x)/xy = 21/xy

4y + 9x = 21

now we got two equations : 

first is : 2y + 3x = 9

and second is : 4y + 9x = 21

now in the first equation : multiply the both sides with 2 

u would get : 

2( 2y + 3x ) =18

4y  + 6x = 18 

4y  + 9y = 21

now subtract 1st equation from 2nd : 

(4y + 9y) - ( 4y + 6x ) = 21 - 18

4y + 9y - 4y - 6x = 3

3x = 3

x = 1

now see put the value of x in 1st equation that we have earlier ( 2/x + 3/y = 9/xy )

2 + 3/y = 9/y

(2y+3)/y = 9/y

2y+3 = 9 

2y = 6

y = 3 

  • 6

taking first polynnomial , 2/x+3/y=9/xy

now taking LCM at LHS , we get,( 2y+3x) /xy=9/xy 

xy will cancel out by xy at RHS and we get a simple eqation,  2y+3x=9

similarly doing same procedure with other polynomial, we get the eq.,4y+9x=21

after solving these eq.;s we get ,y=3 and x=1

  • 4
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