How do i use elimination process when solving two variable equations?

Solve simultaneously:

15x-8y=52 and
6x+14y=38

Let's solve this system thru elimination by addition/subtraction:

Let's get rid of the x terms.
To do this, mult. the first eqn. by -6 and the second by 15.  (This is not the only way in which we can do this!!)  We get  

-90x + 48y = -312
90x   +210y = 570

Add all 3 columns together.  We end up with:

258y = 258, so y = 1.  You can find x by subst. 1 for y in either of the given equations.

If you'd like more help, please be specific about what you want.