here the difference is in first case we will not get a unique solution of the equation but in second case we will get it.
here is how,
in first question both of the statements gives the following equation
4x+3y=250 ..considering x as price of rolls & y is that of doughnuts
now there are more than one solution possible for x and y like (100,150) ,(4,246) etc
so we cannot zero on the solution .hence the ans is E

in second case from statement 2 we get
23x+21y=130 ..
only x=2 and y=4 satisfies this.hence we can say for sure that number of 23 cents pencil is 2...so ans is B

hopes this clarifies the confusion.

Thanks for your prompt reply

One last question how can we know if there is one solution \ combination or different combinations to the equation.
Is it by trial and error or is there a specific rule?

I have noticed that in 21x + 23y = 130 (23 is a prime number)
whereas in 8x + 6y = 500 (no prime number)

Does the existence of a prime number reveals that it will be one combination that solves the equation or it isn't relevant?

whether we can make prime numbers as deciding factors or not I am not sure(and 4x+3y=250 also has prime in it) ,but if you examine the second set closely u will get a particular pattern
in one of the statement we have sum of two variables and in the other we have a different relation involving the two variables.
so clearly we can use these two equations and slove to get a specific value for each variable. But the pattern for these type of questions is for the second relation i.e which does not provide the sum of two numbers usually has unique solution. picking up numbers i think is the only possible way but the good thing is we can restrict the set where the sum of the variables is equal to what is mentioned in first statement. (this is what I have seen so far in these type of questions ..but there might always be some exception)

for the first problem we have only one relation from both statements and here also i used picking up numbers to check if the solution is unique.
we will wait for others reply to see if they can identify any specific pattern or relation in these questions.