Question

$99x + 101y = 499xy \\ 101x + 99y = 501xy \: who \: sloved \: correctly \: i \: will \: mark \: as \: a \: brainest$

Answer 1

Given:

99x + 101y = 499xy ------- (1)

Given:

101x + 99y = 501xy  ----- (2)


Now,

On adding  (1) & (2), we get

99x + 101y + 101x + 99y = 499xy + 501xy

200x + 200y = 1000xy

x + y = 5xy    -------------- (3)


On subtracting (1) & (2), we get

99x + 101y - 101x - 99y = 499xy - 501xy

-2x + 2y = -2xy

x - y = xy ------- (4)


On solving (3) & (4), we get

x + y = 5xy

x - y = xy
----------------

2y = 4xy

2y/4y = x

1/2 = x.



Substitute x = 1/2 in (3), we get

x + y = 5xy

1/2 + y = 5(1/2)y

1/2 + y = 5y/2

1 + 2y = 5y

1 = 5y - 2y

1 = 3y

y = 1/3.



Therefore x = 1/2 and y = 1/3.


Hope this helps!