Find two mixed numbers so that the sum is 8 4/8 and the difference is 2 2/8

The numbers are x and y; 

we suggest this system of equations:

x+y= 8  4/8
x-y=2  2/8

we solve this problem by reduction method.

x+y= 8  4/8
x-y=2  2/8

2x  =  10 6/8    ⇒x=10/2   (6/8)/2=5   3/8

  x+y= 8  4/8
-(x-y=2  2/8)

     2y=6   2/8     ⇒y=6/2  (2/8)/2=3  1/8

the numbers are  5  3/8  and   3  1/8.

To check:
the sum is :  5  3/8  +  3  1/8  =8  4/8
The difference is : 5  3/8  -  3  1/8=2  2/8

Dis the solution here