Look through both equations to find the term that contains
a letter that has the smallest coefficient (in absolute value).


That is the term -y in the first equation

Solve it for y.  Add -4x to both sides:

     4x-y=17
    -4x     -4x
    -----------
       -y=17-4x

Solve for y by dividing every term by the
coefficient of y which is -1

        y=-17+4x

Next take the other equation, the one you haven't used,

      -9x+8y=2

and replace y by the right side of the previous equation,
placed in parentheses like this: (-17+4x)


So 

      -9x+8y=2

becomes

      -9x+8(-17+4x)=2

Then you solve that for x

        -9x-136+32x=2
         
Combine like terms:

           -136+23x=2

Add 136 to both sides:

           -136+23x =  2
            136      136
           -------------
               23x = 138

Divide both sides by 23

                 x = 6
            
Go back to the equation

           y=-17+4x
     
and substitute (6) for x

        y=-17+4(6)
        y=-17+24
        y=7

So the solution is x=6, y=7, sometimes written

(x,y) = (6,7)

Edwin