Question

Find the values of (x + y) and (x – y) of the following given simultaneous equations:

101x + 99y = 501 

99x + 101y = 499

Answer 1

101x + 99y = 501   ...(1)

99x + 101y = 499   ...(2)

Adding equations (1) and (2),

101x +   99y =   501   ...(1)
  99x + 101y =   499  ...(2)
200x + 200y = 1000

∴ x + y = 5   ...(Dividing both the sides by 200)

Subtracting equation (2) from equation (1),

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

∴ x – y = 1   ...(Dividing both the sides by 2)

The value of (x + y) is 5; the value of (x – y) is 1.