SOLUTION: A small-town library buys a total of 33 books that cost $966. Some of the books cost $22 each, and the remainder cost $34 each. How many books of each price did the library buy?

Question 888602: A small-town library buys a total of 33 books that cost $966. Some of the books cost $22 each, and the remainder cost $34 each. How many books of each price did the library buy?
and
Solve the system by using either the substitution or the elimination-by-addition method, whichever seems more appropriate. (Objective 1. If there are infinitely many solutions, enter INFINITELY MANY. If the system is inconsistent, enter INCONSISTENT.)
(2x-5y=6)
(y=2/5x-6/5)
(x,y)=( , )

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
x+y=33
22x+34y=966
1,1,33
22,34,966
divide row 1 by 1/1
1,1,33
22,34,966
add down (-22/1) *row 1 to row 2
1,1,33
0,12,240
divide row 2 by 12/1
1,1,33
0,1,20
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (-1/1) *row 2 to row 1
1,0,13
0,1,20
final
1,0,13
0,1,20
13 at $22
20 at $34

(2x-5y=6)
(y=2/5x-6/5)
5y=2x-6
2x-5y-6=0
2x-5y=6
They are the same equations so there are INFINITELY MANY

RELATED QUESTIONS
A small town library buys a total of 32 books that cost $458. Some of the books cost $13... (answered by SHUgrad05)

a local library bought 54 books. some cost $32 each and some cost $44 each. the total... (answered by jim_thompson5910)

2 algebra books and 3 geometry books cost $ 34, and 2 algebra books and 2 geometry books... (answered by ikleyn)

martin and anna buy books at a sale. martin buys 3 hardcover books and 4 paperback books... (answered by checkley75)

Mike and Sarah buy books at a sale. Mike buys 3 hardcover books and 4 paperback books... (answered by checkley79)

15 books are being bought. Some cost $8.50 each, the remainder cost $9.50 each. Estimate... (answered by Nate)

fred buys a box of books at a car boot sale the box contains 7 hardback books and 8 soft... (answered by edjones)

please help me solve my word problem {nine books are to be bought by a student. Some cost (answered by josgarithmetic,addingup)

A man bought 15 books for #9800. Some of these books cost #600 each and the rest cost... (answered by josgarithmetic)