Question

Solve the linear system using elimination.
10x-9y=46
-2x+3y=10

Answer 1

multiply the second equation all the way across by 3, then add the two together and the y terms will go bye bye

Answer 2

so x=4?

Answer 3

yes

Answer 4

but 10(4)-9y wont equal 46

Answer 5

you have to solve for y

Answer 6

ok so 40-9y=46. 9y=6?

Answer 7

oh i was wrong it is not x = 4

Answer 8

\[4x=76\]

Answer 9

when you add

Answer 10

so \(x=19\) not \(4\)

Answer 11

sorry about that

Answer 12

so 10x-8y=46
-6x+9y=30

Answer 13

\[10x-9y=46\\ -6x+9y=30\]

Answer 14

y=16?

Answer 15

\[4x=76\\
x=19\]

Answer 16

therefore, if x=19, y=16

Answer 17

yes

Answer 18

Thank you! Can you please help me with a couple more?

Answer 19

sure if i can

Answer 20

8x-5y=11
4x-3y=5

Answer 21

this one is ok too, multipliy the second one by \(-2\) then add

Answer 22

why -2?

Answer 23

because then you will have \(8x\) and \(-8x\)

Answer 24

this is actually what you are supposed to be learning, what to multiply by to eliminate one of the variables

Answer 25

so y=1, then I solve for x

Answer 26

x=2?

Answer 27

yes

Answer 28

how about this one.

11x-20y=28
3x=4y=36

Answer 29

too many equal signs

Answer 30

whoops! 3x+4y=36

Answer 31

ok now it is your turn
figure out what to multiply the second one by to get rid of one of the variables

Answer 32

5?

Answer 33

yes

Answer 34

so 11x-20y=28
15x+20y=36

Answer 35

right and now if you add the y terms go away
that is what you are learning here

Answer 36

so 15x=180

Answer 37

hold on

Answer 38

i think there is a mistake somewhere
did you multiply both sides by 5?

Answer 39

both equation 1 and 2 no, but I multiplied 3x, 4y, and 36 by 5

Answer 40

so you have \[11x-20y=28\\
15x+20y=180
\]

Answer 41

yes

Answer 42

add and get what?

Answer 43

26x=208

Answer 44

so does x=8 and y=3?

Answer 45

yes

Answer 46

this next one is a word problem

Answer 47

great

Answer 48

A library is having a book sale to raise money. Hardcover books cost $4 each and paperback books cost $2 each. A person spends $26 dollars for 8 books. How many hardcover books did she purchase?

Answer 49

you can do this a bunch of ways, but i guess they want you to write two linear equation
the total is 8 books so if x is the hard cover, y the paper back then \[x+y=8\]

Answer 50

the total cost is 26 so using the above variables you have \[4x+2y=26\] solve that system

Answer 51

x=5 and y=3?

Answer 52

yeah an easy check

Answer 53

\[5+3=8\\

4\times 5+2\times 3=26\]

Answer 54

What about this one? A website allows users to download individual songs or an entire album. All individual songs cost the same to download, and all album cost the same to download./ Ryan pays $14.94 to download 5 individual songs and 1 album. Seth pays $22.95 to download 3 individual songs and 2 albums. How much does the website charge to download a songs? An entire album?

Answer 55

you want to try the two equations

Answer 56

how do I get them though?

Answer 57

i will do the first, you can do the second

Answer 58

if x is songs, y is lps then \[5x+y=14.95\]

Answer 59

so 3x+2y=$22.95

Answer 60

yup

Answer 61

how do I solve it

Answer 62

\[3x+2y=22.95\\
5x+y=14.95\]go ahead and figure out what to multiply the second one by to eliminate the y

Answer 63

2

Answer 64

actually \(-2\)