Astudent has some $1 and $5 bills in his wallet. he has a total of 1919 bills that are worth $5959. how many of each type of bill does he hav

A = number of $1 bill
B = number of $5 bill

A + B = 1919
A*$1 + B*$5 = 5959

so 

A + B = 1919
A + 5B = 5959

Substract both equation

A + 5B - (A + B) = 5959 - 1919
4B = 4040

B = 1010

And
A = 1919 - B = 1919 - 1010 = 909
A = 909

Check the result : 

A*$1 + B*$5 = 909 + 1010*5 = 909 + 5050 = 5959