Math help! Linear systems...

I'm a freshman in hs nd yes this still confuses me ! Here's my problem. Can you help??

You and your friend each purchased identical subscriptions to an online video rental site. When you joined, you each paid the one-time membership processing fee. You also paid a flat rate for each movie that you downloaded. By the end of the first month, you had downloaded 8 movies and paid $16.50, while your friend had downloaded only 6 movies and paid $14.00.
Write and solve a system of linear equations to answer the questions below. Document your work to support your answer.
1. What was the one-time membership processing fee?
2. What was the per-movie rental fee?

Let X be the one time subscription fee and Y be the flat rate per movie downloaded, then the system of equations is this:

$16.50 = X + 8Y
$14.00 = X + 6Y

You have two equations and two variables. I would solve by elimination.

First, multiply the 2nd equation by -1.

-$14.00 = -X - 6Y

Add the two equations together

$16.50 = X + 8Y
-$14.00 = -X - 6Y
----------------------------
$2.50 = 2Y
Y = $1.25

The flat fee per movie is $1.25. Now that you know Y, plug it in to either equation to find X.

$16.50 = X + 8($1.25)
$16.50 = X + $10
X = $6.50

The subscription fee is $6.50