Question

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

Answer 1

Let us use a  trick to solve it quickly

99x + 101y = 499 ............ i

101x + 99y = 501............ ii

subtract i  from  ii

2x - 2y = 2      or          x - y =1  or       x = 1 + y   ....... ..............................................   iii

add i and  ii

200x + 200y = 1000      or         x + y = 5  ...................................................................... iv

Now from iii and  iv  ,  we get  1 + y + y = 5       or          2y = 4       or        y = 2     ......  v

again from iii and  v   , we get  x = 1 + 2 = 3

Hence x = 3  ,  y = 2