<< Chapter < Page Chapter >> Page >

5 x y = 4 x + 6 y = 2 and ( 4 , 0 )

Got questions? Get instant answers now!

−3 x 5 y = 13   x + 4 y = 10 and ( −6 , 1 )

Yes

Got questions? Get instant answers now!

3 x + 7 y = 1 2 x + 4 y = 0 and ( 2 , 3 )

Got questions? Get instant answers now!

−2 x + 5 y = 7    2 x + 9 y = 7 and ( −1 , 1 )

Yes

Got questions? Get instant answers now!

x + 8 y = 43 3 x −2 y = −1 and ( 3 , 5 )

Got questions? Get instant answers now!

For the following exercises, solve each system by substitution.

   x + 3 y = 5 2 x + 3 y = 4

( −1 , 2 )

Got questions? Get instant answers now!

  3 x −2 y = 18 5 x + 10 y = −10

Got questions? Get instant answers now!

4 x + 2 y = −10 3 x + 9 y = 0

( −3 , 1 )

Got questions? Get instant answers now!

2 x + 4 y = −3.8 9 x −5 y = 1.3

Got questions? Get instant answers now!

2 x + 3 y = 1.2 3 x 6 y = 1.8

( 3 5 , 0 )

Got questions? Get instant answers now!

    x −0.2 y = 1 −10 x + 2 y = 5

Got questions? Get instant answers now!

     3 x + 5 y = 9 30 x + 50 y = −90

No solutions exist.

Got questions? Get instant answers now!

  −3 x + y = 2 12 x −4 y = −8

Got questions? Get instant answers now!

1 2 x + 1 3 y = 16 1 6 x + 1 4 y = 9

( 72 5 , 132 5 )

Got questions? Get instant answers now!

1 4 x + 3 2 y = 11 1 8 x + 1 3 y = 3

Got questions? Get instant answers now!

For the following exercises, solve each system by addition.

−2 x + 5 y = −42    7 x + 2 y = 30

( 6 , −6 )

Got questions? Get instant answers now!

6 x −5 y = −34 2 x + 6 y = 4

Got questions? Get instant answers now!

     5 x y = −2.6 −4 x −6 y = 1.4

( 1 2 , 1 10 )

Got questions? Get instant answers now!

7 x −2 y = 3 4 x + 5 y = 3.25

Got questions? Get instant answers now!

  −x + 2 y = −1 5 x −10 y = 6

No solutions exist.

Got questions? Get instant answers now!

       7 x + 6 y = 2 −28 x −24 y = −8

Got questions? Get instant answers now!

5 6 x + 1 4 y = 0 1 8 x 1 2 y = 43 120

( 1 5 , 2 3 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

−0.2 x + 0.4 y = 0.6             x −2 y = −3

( x , x + 3 2 )

Got questions? Get instant answers now!

−0.1 x + 0.2 y = 0.6       5 x −10 y = 1

Got questions? Get instant answers now!

For the following exercises, solve each system by any method.

5 x + 9 y = 16    x + 2 y = 4

( −4 , 4 )

Got questions? Get instant answers now!

6 x −8 y = −0.6 3 x + 2 y = 0.9

Got questions? Get instant answers now!

5 x −2 y = 2.25 7 x −4 y = 3

( 1 2 , 1 8 )

Got questions? Get instant answers now!

   x 5 12 y = 55 12 −6 x + 5 2 y = 55 2

Got questions? Get instant answers now!

7 x −4 y = 7 6 2 x + 4 y = 1 3

( 1 6 , 0 )

Got questions? Get instant answers now!

3 x + 6 y = 11 2 x + 4 y = 9

Got questions? Get instant answers now!

       7 3 x 1 6 y = 2 21 6 x + 3 12 y = −3

( x , 2 ( 7 x −6 ) )

Got questions? Get instant answers now!

1 2 x + 1 3 y = 1 3 3 2 x + 1 4 y = 1 8

Got questions? Get instant answers now!

2.2 x + 1.3 y = −0.1 4.2 x + 4.2 y = 2.1

( 5 6 , 4 3 )

Got questions? Get instant answers now!

  0.1 x + 0.2 y = 2 0.35 x −0.3 y = 0

Got questions? Get instant answers now!

Graphical

For the following exercises, graph the system of equations and state whether the system is consistent, inconsistent, or dependent and whether the system has one solution, no solution, or infinite solutions.

3 x y = 0.6 x −2 y = 1.3

Consistent with one solution

Got questions? Get instant answers now!

x + 2 y = 4   2 x −4 y = 1

Got questions? Get instant answers now!

   x + 2 y = 7 2 x + 6 y = 12

Consistent with one solution

Got questions? Get instant answers now!

3 x −5 y = 7    x −2 y = 3

Got questions? Get instant answers now!

   3 x −2 y = 5 −9 x + 6 y = −15

Dependent with infinitely many solutions

Got questions? Get instant answers now!

Technology

For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth.

    0.1 x + 0.2 y = 0.3 −0.3 x + 0.5 y = 1

Got questions? Get instant answers now!

−0.01 x + 0.12 y = 0.62 0.15 x + 0.20 y = 0.52

( −3.08 , 4.91 )

Got questions? Get instant answers now!

0.5 x + 0.3 y = 4 0.25 x −0.9 y = 0.46

Got questions? Get instant answers now!

0.15 x + 0.27 y = 0.39 −0.34 x + 0.56 y = 1.8

( −1.52 , 2.29 )

Got questions? Get instant answers now!

−0.71 x + 0.92 y = 0.13 0.83 x + 0.05 y = 2.1

Got questions? Get instant answers now!

Extensions

For the following exercises, solve each system in terms of A , B , C , D , E , and F where A F are nonzero numbers. Note that A B and A E B D .

x + y = A x y = B

( A + B 2 , A B 2 )

Got questions? Get instant answers now!

A x + y = 0 B x + y = 1

( −1 A B , A A B )

Got questions? Get instant answers now!

A x + B y = C D x + E y = F

( C E B F B D A E , A F C D B D A E )

Got questions? Get instant answers now!

Real-world applications

For the following exercises, solve for the desired quantity.

A stuffed animal business has a total cost of production C = 12 x + 30 and a revenue function R = 20 x . Find the break-even point.

Got questions? Get instant answers now!

A fast-food restaurant has a cost of production C ( x ) = 11 x + 120 and a revenue function R ( x ) = 5 x . When does the company start to turn a profit?

They never turn a profit.

Got questions? Get instant answers now!

A cell phone factory has a cost of production C ( x ) = 150 x + 10 , 000 and a revenue function R ( x ) = 200 x . What is the break-even point?

Got questions? Get instant answers now!

A musician charges C ( x ) = 64 x + 20,000 , where x is the total number of attendees at the concert. The venue charges $80 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point?

( 1 , 250 , 100 , 000 )

Got questions? Get instant answers now!

A guitar factory has a cost of production C ( x ) = 75 x + 50,000. If the company needs to break even after 150 units sold, at what price should they sell each guitar? Round up to the nearest dollar, and write the revenue function.

Got questions? Get instant answers now!

Questions & Answers

the diagram of the digestive system
Assiatu Reply
allimentary cannel
Ogenrwot
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Condoleezza Reply
what is cell divisoin?
Aron Reply
Diversity of living thing
ISCONT
what is cell division
Aron Reply
Cell division is the process by which a single cell divides into two or more daughter cells. It is a fundamental process in all living organisms and is essential for growth, development, and reproduction. Cell division can occur through either mitosis or meiosis.
AI-Robot
What is life?
Allison Reply
life is defined as any system capable of performing functions such as eating, metabolizing,excreting,breathing,moving,Growing,reproducing,and responding to external stimuli.
Mohamed
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




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