I love math! Hope i can be of some help. One way yo solve may be:

1st: You must get on of the variables (either x or y) by itself on one side of the equal sign. *I will choose x, since in this equation it will be the simplest.

the 3y is a negative ( because there's a "-" subtraction sign in front of it), so to cancel it out you must "+" ADD 3y. what you do to one side of the equation, you must do to the other, so you must "+" add 3y to the 8, too.  

your work should look like this:     x-3y=8

                                                  +3y  +3y
                                               _________

your result will look like this:           x= 8 +3y 

According to your results, x is EQUAL to 8 + 3y. Thus, you can SUBSTITUTE the new value of x into original equation (x-3y=8).

Look at the original equation: x-3y=8 ...you know that x also equals 8+3y (you got this from your result), so you can REPLACE the x with 8+3y.

Should look like this: x-3y=8 --> (8+3y) -3y=8

Now, add the numbers on the left side of the "=" equal sign.  the 3y and -3y equal zero when they are add. so you are left with 8=8.