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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

Discuss the differences between taste and flavor, including how other sensory inputs contribute to our  perception of flavor.
John Reply
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Ummi Reply
omeprazole
Kamara
what
Renee
what is this
Renee
is a drug
Kamara
of anti-ulcer
Kamara
Omeprazole Cimetidine / Tagament For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
Nency Reply
Not really sure
Eli
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
what is anatomy
Oyindarmola Reply
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Oyerinde Reply
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Mohammed Reply
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
Wulku Reply
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
Ali Reply
function of digestive
Ali
the diagram of the lungs
Adaeze Reply
what is the normal body temperature
Diya Reply
37 degrees selcius
Xolo
37°c
Stephanie
please why 37 degree selcius normal temperature
Mark
36.5
Simon
37°c
Iyogho
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
37A c
Wulku
what is anaemia
Diya Reply
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
Diya Reply
how does Lysin attack pathogens
Diya
acid
Mary
I information on anatomy position and digestive system and there enzyme
Elisha Reply
anatomy of the female external genitalia
Muhammad Reply
Organ Systems Of The Human Body (Continued) Organ Systems Of The Human Body (Continued)
Theophilus Reply
what's lochia albra
Kizito
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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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