<< Chapter < Page Chapter >> Page >

[ 3 4 10 17    |    10 439 ]

Got questions? Get instant answers now!

[ 3 2 0 −1 −9 4 8 5 7    |    3 −1 8 ]

3 x + 2 y = 13 x −9 y + 4 z = 53 8 x + 5 y + 7 z = 80

Got questions? Get instant answers now!

[ 8 29 1 −1 7 5 0 0 3    |    43 38 10 ]

Got questions? Get instant answers now!

[ 4 5 −2 0 1 58 8 7 −3    |    12 2 −5 ]

4 x + 5 y −2 z = 12          y + 58 z = 2 8 x + 7 y −3 z = −5

Got questions? Get instant answers now!

For the following exercises, solve the system by Gaussian elimination.

[ 1 0 0 0    |    3 0 ]

Got questions? Get instant answers now!

[ 1 0 1 0    |    1 2 ]

No solutions

Got questions? Get instant answers now!

[ 1 2 4 5    |    3 6 ]

Got questions? Get instant answers now!

[ −1 2 4 −5    |    −3 6 ]

( −1 , −2 )

Got questions? Get instant answers now!

[ −2 0 0 2    |    1 −1 ]

Got questions? Get instant answers now!

   2 x 3 y = 9 5 x + 4 y = 58

( 6 , 7 )

Got questions? Get instant answers now!

6 x + 2 y = −4 3 x + 4 y = −17

Got questions? Get instant answers now!

2 x + 3 y = 12    4 x + y = 14

( 3 , 2 )

Got questions? Get instant answers now!

−4 x −3 y = −2    3 x −5 y = −13

Got questions? Get instant answers now!

−5 x + 8 y = 3 10 x + 6 y = 5

( 1 5 , 1 2 )

Got questions? Get instant answers now!

   3 x + 4 y = 12 −6 x −8 y = −24

Got questions? Get instant answers now!

−60 x + 45 y = 12    20 x −15 y = −4

( x , 4 15 ( 5 x + 1 ) )

Got questions? Get instant answers now!

11 x + 10 y = 43 15 x + 20 y = 65

Got questions? Get instant answers now!

  2 x y = 2 3 x + 2 y = 17

( 3 , 4 )

Got questions? Get instant answers now!

−1.06 x −2.25 y = 5.51 −5.03 x −1.08 y = 5.40

Got questions? Get instant answers now!

3 4 x 3 5 y = 4 1 4 x + 2 3 y = 1

( 196 39 , 5 13 )

Got questions? Get instant answers now!

1 4 x 2 3 y = −1 1 2 x + 1 3 y = 3

Got questions? Get instant answers now!

[ 1 0 0 0 1 1 0 0 1    |    31 45 87 ]

( 31 , −42 , 87 )

Got questions? Get instant answers now!

[ 1 0 1 1 1 0 0 1 1    |    50 20 −90 ]

Got questions? Get instant answers now!

[ 1 2 3 0 5 6 0 0 8    |    4 7 9 ]

( 21 40 , 1 20 , 9 8 )

Got questions? Get instant answers now!

[ −0.1 0.3 −0.1 −0.4 0.2 0.1 0.6 0.1 0.7    |    0.2 0.8 −0.8 ]

Got questions? Get instant answers now!

  −2 x + 3 y 2 z = 3        4 x + 2 y z = 9       4 x 8 y + 2 z = −6

( 18 13 , 15 13 , 15 13 )

Got questions? Get instant answers now!

       x + y 4 z = −4    5 x 3 y 2 z = 0    2 x + 6 y + 7 z = 30

Got questions? Get instant answers now!

       2 x + 3 y + 2 z = 1    −4 x 6 y 4 z = −2   10 x + 15 y + 10 z = 5

( x , y , 1 2 ( 1 −2 x −3 y ) )

Got questions? Get instant answers now!

     x + 2 y z = 1 x 2 y + 2 z = −2 3 x + 6 y 3 z = 5

Got questions? Get instant answers now!

     x + 2 y z = 1 x −2 y + 2 z = −2   3 x + 6 y −3 z = 3

( x , x 2 , −1 )

Got questions? Get instant answers now!

    x + y = 2     x + z = 1 y z = −3

Got questions? Get instant answers now!

x + y + z = 100      x + 2 z = 125 y + 2 z = 25

( 125 , −25 , 0 )

Got questions? Get instant answers now!

1 4 x 2 3 z = 1 2 1 5 x + 1 3 y = 4 7 1 5 y 1 3 z = 2 9

Got questions? Get instant answers now!

1 2 x + 1 2 y + 1 7 z = 53 14     1 2 x 1 2 y + 1 4 z = 3      1 4 x + 1 5 y + 1 3 z = 23 15

( 8 , 1 , −2 )

Got questions? Get instant answers now!

1 2 x 1 3 y + 1 4 z = 29 6     1 5 x + 1 6 y 1 7 z = 431 210 1 8 x + 1 9 y + 1 10 z = 49 45

Got questions? Get instant answers now!

Extensions

For the following exercises, use Gaussian elimination to solve the system.

x −1 7 + y −2 8 + z −3 4 = 0                       x + y + z = 6       x + 2 3 + 2 y + z −3 3 = 5

( 1 , 2 , 3 )

Got questions? Get instant answers now!

x −1 4 y + 1 4 + 3 z = −1     x + 5 2 + y + 7 4 z = 4           x + y z −2 2 = 1

Got questions? Get instant answers now!

       x −3 4 y −1 3 + 2 z = −1 x + 5 2 + y + 5 2 + z + 5 2 = 8                       x + y + z = 1

( x , 31 28 3 x 4 , 1 28 ( −7 x −3 ) )

Got questions? Get instant answers now!

x −3 10 + y + 3 2 −2 z = 3   x + 5 4 y −1 8 + z = 3 2 x −1 4 + y + 4 2 + 3 z = 3 2

Got questions? Get instant answers now!

      x −3 4 y −1 3 + 2 z = −1 x + 5 2 + y + 5 2 + z + 5 2 = 7                       x + y + z = 1

No solutions exist.

Got questions? Get instant answers now!

Real-world applications

For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution.

Every day, a cupcake store sells 5,000 cupcakes in chocolate and vanilla flavors. If the chocolate flavor is 3 times as popular as the vanilla flavor, how many of each cupcake sell per day?

Got questions? Get instant answers now!

At a competing cupcake store, $4,520 worth of cupcakes are sold daily. The chocolate cupcakes cost $2.25 and the red velvet cupcakes cost $1.75. If the total number of cupcakes sold per day is 2,200, how many of each flavor are sold each day?

860 red velvet, 1,340 chocolate

Got questions? Get instant answers now!

You invested $10,000 into two accounts: one that has simple 3% interest, the other with 2.5% interest. If your total interest payment after one year was $283.50, how much was in each account after the year passed?

Got questions? Get instant answers now!

You invested $2,300 into account 1, and $2,700 into account 2. If the total amount of interest after one year is $254, and account 2 has 1.5 times the interest rate of account 1, what are the interest rates? Assume simple interest rates.

4% for account 1, 6% for account 2

Got questions? Get instant answers now!

Bikes’R’Us manufactures bikes, which sell for $250. It costs the manufacturer $180 per bike, plus a startup fee of $3,500. After how many bikes sold will the manufacturer break even?

Got questions? Get instant answers now!

A major appliance store is considering purchasing vacuums from a small manufacturer. The store would be able to purchase the vacuums for $86 each, with a delivery fee of $9,200, regardless of how many vacuums are sold. If the store needs to start seeing a profit after 230 units are sold, how much should they charge for the vacuums?

$126

Got questions? Get instant answers now!

The three most popular ice cream flavors are chocolate, strawberry, and vanilla, comprising 83% of the flavors sold at an ice cream shop. If vanilla sells 1% more than twice strawberry, and chocolate sells 11% more than vanilla, how much of the total ice cream consumption are the vanilla, chocolate, and strawberry flavors?

Got questions? Get instant answers now!

At an ice cream shop, three flavors are increasing in demand. Last year, banana, pumpkin, and rocky road ice cream made up 12% of total ice cream sales. This year, the same three ice creams made up 16.9% of ice cream sales. The rocky road sales doubled, the banana sales increased by 50%, and the pumpkin sales increased by 20%. If the rocky road ice cream had one less percent of sales than the banana ice cream, find out the percentage of ice cream sales each individual ice cream made last year.

Banana was 3%, pumpkin was 7%, and rocky road was 2%

Got questions? Get instant answers now!

A bag of mixed nuts contains cashews, pistachios, and almonds. There are 1,000 total nuts in the bag, and there are 100 less almonds than pistachios. The cashews weigh 3 g, pistachios weigh 4 g, and almonds weigh 5 g. If the bag weighs 3.7 kg, find out how many of each type of nut is in the bag.

Got questions? Get instant answers now!

A bag of mixed nuts contains cashews, pistachios, and almonds. Originally there were 900 nuts in the bag. 30% of the almonds, 20% of the cashews, and 10% of the pistachios were eaten, and now there are 770 nuts left in the bag. Originally, there were 100 more cashews than almonds. Figure out how many of each type of nut was in the bag to begin with.

100 almonds, 200 cashews, 600 pistachios

Got questions? Get instant answers now!

Questions & Answers

An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Kala Reply
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply
12, 17, 22.... 25th term
Alexandra Reply
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Shirleen Reply
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
Practice Key Terms 7

Get the best College algebra course in your pocket!





Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College algebra' conversation and receive update notifications?

Ask