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`

∴ x = 3

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

x + y = 5

∴ 3 + y = 5

∴ y = 5 – 3

∴ y = 2

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