Question

Solve: 99x + 101y = 499, 101x + 99y = 501

Answer 1

The given equations are

99x + 101y = 499    .....(i)

101x + 99y = 501   .....(ii)

Adding equations (i) and (ii), we get

      99x + 101y = 499
+ 101x +    99y = 501    
   200x +  200y = 1000

∴ x + y = `1000/200`   ......[Dividing both sides by 200]

∴ x + y = 5     ......(iii)

Subtracting equation (ii) from (i), we get

  99x + 101y = 499
101x +  99y  = 501
  −         −         −    
−2x  +   2y   =−2

∴ x – y = `(-2)/(-2)`     ......[Dividing both sides by – 2]

∴ x − y = 1        .......(iv)

Adding equations (iii) and (iv), we get

    x + y = 5
+ x − y = 1 
   2x     = 6

∴ x = `6/2` = 3

Substituting x = 3 in equation (iii), we get

x + y = 5

∴ 3 + y = 5

∴ y = 5 − 3 = 2

∴ (x, y) = (3, 2) is the solution of the given equations.