Question

solve this equation 99x + 101y = 499 ; 101x + 99y = 501

Answer 1

............I think it is a right answer..............

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

99x + 101y = 499 …………...(1)

101x + 99y = 501 …………...(2)

Now,

Adding (1) and (2) we get,

200x + 200y = 1000

200(x + y) = 1000

x + y = 1000/200

x + y = 5 ………………. (3)

Now,

Subtracting (1) and (2) we get,

-2x + 2y = -2

-2(x - y) = -2

x - y = -2/-2

x - y = 1………….. (4)

Now,

Adding (3) and (4) we get,

2x = 6

x = 6/2

x = 3

Putting value of x in (3)

x + y = 5

3 + y = 5

y = 5 - 3

y = 2

Therefore ,

x = 3 and y = 2