Question

x+y=5xy , 3x+2y = 13xy

Answer 1

Heya user,

-----> x + y = 5xy -----------> (1)
-----> 3x + 2y = 13xy -------> (2)

Now, x + y = 5xy
=> y - 5xy = -x
=> y ( 1 - 5x ) = -x
=> y = x / [ 5x - 1 ]

Now, putting this in (2) -->
---> 3x + { 2x / [ 5x - 1 ] } = 13x² / [5x - 1]
==> 15x² - 3x + 2x = 13x²
==> 2x² - x = 0
==> x = 0; or  x = 1/2

Sooo, y = 0 or y = 1/3 ;

Hence, the solution set is (0,0) or ( 1/2 , 1/3 )

Answer 2

Step-by-step explanation:

First,

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solution are (x,y)=(0,0)

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second,

now dividing both equation by xy

and multiply than adding we get,

the above mention result show in image

now supposing 1/x=a and 1/y=b

than by elimination method we will get another solution

a+b=5

2a+5b=13

b=1

1/y=1

y=1

so,

x=1/4

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solution are (x,y)=(1/4,1)

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