99x+101y = 499...(i)
101x+99y = 501...(ii)
Equation (i) - Equation (ii)
99 x + 101 y - 101 x - 99y = 499 - 501
2y - 2x = -2
x - y =1...(iii)
Equation (i) + Equation (ii)
99 x + 101 y + 101 x + 99y = 499 + 501
200(x+y) = 1000
x + y = 5 ...(iv)
Equation (iii) + Equation (iv)
x -y + x + y = 1+ 5
2x = 6
x = 3
y = 2