Question 831258
What you need to do here is somehow isolate one of the variables.

3x + 14y = 203
11x + 11y = 220

What I would do here is first of all divide the bottom equation by 11:
x + y = 20

Now get one variable by itself.  Either one works; I'll choose y.
y = 20 - x

Now substitute 20-x for y in either equation. I'll pick the first one.
3x + 14(20-x) = 203
3x + 280 - 14x = 203
280 - 11x = 203
280 = 203 + 11x
77 = 11x
x = 7

Which means y = 20-7 or 13.

So your prices are $7 for the small boxes and $13 for the large.

Check:
3(7) + 14(13) =? 203 and 11(7) + 11(13) =? 220
21 + 182 =? 203 and 77 + 143 =? 220
203=203 and 220=220 {{{check}}}