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{ x 3 y = −3 y = 2

( 3 , 2 )

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{ 2 x 2 y = 8 y = −3

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{ 2 x y = −1 x = 1

( 1 , 3 )

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{ x 3 y = −6 x = −3

( −3 , −1 )

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

no solution

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{ x + 3 y = 4 −2 x 6 y = 3

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{ −2 x + 4 y = 4 y = 1 2 x

no solution

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

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{ x = −3 y + 4 2 x + 6 y = 8

no solution

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

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{ 2 x + y = 6 −8 x 4 y = −24

infinitely many solutions

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{ 5 x + 2 y = 7 −10 x 4 y = −14

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{ x + 3 y = −6 4 y = 4 3 x 8

infinitely many solutions

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{ x + 2 y = −6 y = 1 2 x 1

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{ −3 x + 2 y = −2 y = x + 4

( 2 , 2 )

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{ x + 2 y = −2 y = x 1

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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

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

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{ y = −2 x + 1 4 x + 2 y = 8

0 solutions

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

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

0 solutions

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{ 3 x + 4 y = 12 y = −3 x 1

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{ 4 x + 2 y = 10 4 x 2 y = −6

consistent, 1 solution

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

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

infinitely many solutions

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{ y = x + 1 x + y = 1

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{ y = 2 x + 3 2 x y = −3

infinitely many solutions

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

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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.

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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?

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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.

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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?

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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.

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

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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.

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

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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 mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
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Practice Key Terms 7

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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