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
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