Question

99x+101y=499xy 101x+99y=501xy solve pair of linear equations

Answer 1

99x+101y=499.xy ...(1)
101x+99y=501xy. ...(2)

Adding equation (1) and (2).
200x+200y=1000xy
x+y=5.xy ...(3)

Subtracting equation (1) from (2)
2x-2y=2xy
x-y=1.xy ...(4)

Solving equation (3)and (4)
2x=6 xy
1/3=y
2y=4xy
x=1/2

Answer 2

99x + 101y = 499xy eq1
101x + 99y = 501xy eq2

Now first add both eq.

200x + 200y = 1000xy

Take 200 common-2x

x + y = 5xy eq3

Now subtract eq1 and eq2

-2x + 2y = -2xy

Take -2 common

x - y = xy eq4

Now solve eq3 and eq4 we get

2x = 6xy

y = 1/3

Put y in eq4

x - 1/3 = x /3

x - x/3 = 1/3

(3x-x)/3 = 1/3

2x/3 = 1/3

x = 1/2

Answer is x = 1/2 and y = 1/3

Thanks