You can put this solution on YOUR website!
Let x = $20 dishes and y = $45 dishes. So you have this part set up correctly.
Since "need to purchase 250 sets of dishes", this means that the sum of 'x' and 'y' must be 250. So the first equation is
Also, because "One design costs $20 per set and the other $45 per set." and you "have budgeted $6,800 to spend on the dishes", this means that the second equation is
. You have this as your first equation.
Does that help?