<< Chapter < Page Chapter >> Page >

{ x 3 y = −3 y = 2

( 3 , 2 )

Got questions? Get instant answers now!

{ 2 x 2 y = 8 y = −3

Got questions? Get instant answers now!

{ 2 x y = −1 x = 1

( 1 , 3 )

Got questions? Get instant answers now!

{ x 3 y = −6 x = −3

( −3 , −1 )

Got questions? Get instant answers now!

{ 4 x 3 y = 8 8 x 6 y = 14

no solution

Got questions? Get instant answers now!

{ x + 3 y = 4 −2 x 6 y = 3

Got questions? Get instant answers now!

{ −2 x + 4 y = 4 y = 1 2 x

no solution

Got questions? Get instant answers now!

{ 3 x + 5 y = 10 y = 3 5 x + 1

Got questions? Get instant answers now!

{ x = −3 y + 4 2 x + 6 y = 8

no solution

Got questions? Get instant answers now!

{ 4 x = 3 y + 7 8 x 6 y = 14

Got questions? Get instant answers now!

{ 2 x + y = 6 −8 x 4 y = −24

infinitely many solutions

Got questions? Get instant answers now!

{ 5 x + 2 y = 7 −10 x 4 y = −14

Got questions? Get instant answers now!

{ x + 3 y = −6 4 y = 4 3 x 8

infinitely many solutions

Got questions? Get instant answers now!

{ x + 2 y = −6 y = 1 2 x 1

Got questions? Get instant answers now!

{ −3 x + 2 y = −2 y = x + 4

( 2 , 2 )

Got questions? Get instant answers now!

{ x + 2 y = −2 y = x 1

Got questions? Get instant answers now!

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations.

{ y = 2 3 x + 1 −2 x + 3 y = 5

0 solutions

Got questions? Get instant answers now!

{ y = 1 3 x + 2 x 3 y = 9

Got questions? Get instant answers now!

{ y = −2 x + 1 4 x + 2 y = 8

0 solutions

Got questions? Get instant answers now!

{ y = 3 x + 4 9 x 3 y = 18

Got questions? Get instant answers now!

{ y = 2 3 x + 1 2 x 3 y = 7

0 solutions

Got questions? Get instant answers now!

{ 3 x + 4 y = 12 y = −3 x 1

Got questions? Get instant answers now!

{ 4 x + 2 y = 10 4 x 2 y = −6

consistent, 1 solution

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

{ y = 1 2 x + 5 x + 2 y = 10

infinitely many solutions

Got questions? Get instant answers now!

{ y = x + 1 x + y = 1

Got questions? Get instant answers now!

{ y = 2 x + 3 2 x y = −3

infinitely many solutions

Got questions? Get instant answers now!

{ 5 x 2 y = 10 y = 5 2 x 5

Got questions? Get instant answers now!

Solve Applications of Systems of Equations by Graphing In the following exercises, solve.

Molly is making strawberry infused water. For each ounce of strawberry juice, she uses three times as many ounces of water. How many ounces of strawberry juice and how many ounces of water does she need to make 64 ounces of strawberry infused water?

Molly needs 16 ounces of strawberry juice and 48 ounces of water.

Got questions? Get instant answers now!

Jamal is making a snack mix that contains only pretzels and nuts. For every ounce of nuts, he will use 2 ounces of pretzels. How many ounces of pretzels and how many ounces of nuts does he need to make 45 ounces of snack mix?

Got questions? Get instant answers now!

Enrique is making a party mix that contains raisins and nuts. For each ounce of nuts, he uses twice the amount of raisins. How many ounces of nuts and how many ounces of raisins does he need to make 24 ounces of party mix?

Enrique needs 8 ounces of nuts and 16 ounces of water.

Got questions? Get instant answers now!

Owen is making lemonade from concentrate. The number of quarts of water he needs is 4 times the number of quarts of concentrate. How many quarts of water and how many quarts of concentrate does Owen need to make 100 quarts of lemonade?

Got questions? Get instant answers now!

Everyday math

Leo is planning his spring flower garden. He wants to plant tulip and daffodil bulbs. He will plant 6 times as many daffodil bulbs as tulip bulbs. If he wants to plant 350 bulbs, how many tulip bulbs and how many daffodil bulbs should he plant?

Leo should plant 50 tulips and 300 daffodils.

Got questions? Get instant answers now!

A marketing company surveys 1,200 people. They surveyed twice as many females as males. How many males and females did they survey?

Got questions? Get instant answers now!

Writing exercises

In a system of linear equations, the two equations have the same slope. Describe the possible solutions to the system.

There is an infinite number of possible solutions to the system of equations.

Got questions? Get instant answers now!

In a system of linear equations, the two equations have the same intercepts. Describe the possible solutions to the system.

Got questions? Get instant answers now!

Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This figure shows a table with four rows and four columns. The columns are labeled, “I can…,” “Confidently.” “With some help.” and “No - I don’t get it.” The only column with filled in cells below it is labeled “I can…” It reads, “determine whether an ordered pair is a solution of a system of equations.” “solve a system of linear equations by graphing.” “determine the number of solutions of a linear system.” and “solve applications of systems of equations by graphing.”

If most of your checks were:

…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.

…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no - I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.

Questions & Answers

what is phylogeny
Odigie Reply
evolutionary history and relationship of an organism or group of organisms
AI-Robot
ok
Deng
what is biology
Hajah Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
what is biology
Victoria Reply
HOW CAN MAN ORGAN FUNCTION
Alfred Reply
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 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
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 7

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

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

Ask