please tell me how to solve this problem. 

 x     y
--- + --- = 1
 8     2

Solve?  It has two unknowns, not just one.  So you can't solve and get 
just a single number value for either x or y. You didn't say what you 
are to solve it for.  Do you want to solve it for x?  Or solve it for 
y? Or graph it? 

Suppose you want to solve it for one of the letters x or y:

 x     y     1
--- + --- = ---
 8     2     1

The LCD is 8, so multiply every term, on the left and
right by 8, written as 8/1

 8   x     8   y     8   1
---·--- + ---·--- = ---·---
 1   8     1   2     1   1

Do some cancelling:

 1         4
 8   x     8   y     8   1
---·--- + ---·--- = ---·---
 1   8     1   2     1   1
     1         1

The denominators are all 1's so you can just write

    x + 4y = 8

If you want to solve for y, then

        4y = 8 - x

Divide every term by 4

         y = 2 - x/4         

If you want to solve for x, then

         x = 8 - 4y

If you want to graph it, find and plot 
the two points:
(0,2) and (8,0) and draw a line
thru them

 

Edwin