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

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

Yes

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

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

Yes

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

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For the following exercises, solve each system by substitution.

   x + 3 y = 5 2 x + 3 y = 4

( −1 , 2 )

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  3 x −2 y = 18 5 x + 10 y = −10

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4 x + 2 y = −10 3 x + 9 y = 0

( −3 , 1 )

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2 x + 4 y = −3.8 9 x −5 y = 1.3

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

( 3 5 , 0 )

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    x −0.2 y = 1 −10 x + 2 y = 5

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     3 x + 5 y = 9 30 x + 50 y = −90

No solutions exist.

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  −3 x + y = 2 12 x −4 y = −8

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

( 72 5 , 132 5 )

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

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For the following exercises, solve each system by addition.

−2 x + 5 y = −42    7 x + 2 y = 30

( 6 , −6 )

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6 x −5 y = −34 2 x + 6 y = 4

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     5 x y = −2.6 −4 x −6 y = 1.4

( 1 2 , 1 10 )

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7 x −2 y = 3 4 x + 5 y = 3.25

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  −x + 2 y = −1 5 x −10 y = 6

No solutions exist.

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       7 x + 6 y = 2 −28 x −24 y = −8

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

( 1 5 , 2 3 )

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

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

( x , x + 3 2 )

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

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

5 x + 9 y = 16    x + 2 y = 4

( −4 , 4 )

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6 x −8 y = −0.6 3 x + 2 y = 0.9

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5 x −2 y = 2.25 7 x −4 y = 3

( 1 2 , 1 8 )

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

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7 x −4 y = 7 6 2 x + 4 y = 1 3

( 1 6 , 0 )

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

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

( x , 2 ( 7 x −6 ) )

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

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

( 5 6 , 4 3 )

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  0.1 x + 0.2 y = 2 0.35 x −0.3 y = 0

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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

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x + 2 y = 4   2 x −4 y = 1

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   x + 2 y = 7 2 x + 6 y = 12

Consistent with one solution

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3 x −5 y = 7    x −2 y = 3

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   3 x −2 y = 5 −9 x + 6 y = −15

Dependent with infinitely many solutions

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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

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

( −3.08 , 4.91 )

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

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

( −1.52 , 2.29 )

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

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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 )

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

( −1 A B , A A B )

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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 )

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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.

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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.

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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?

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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 )

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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.

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Questions & Answers

what is mutation
Janga Reply
what is a cell
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how is urine form
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classification of plants, gymnosperm features.
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how many types of solid did we have
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what is an ionic bond
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What is Atoms
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what is fallopian tube
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what is bladder
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what's bulbourethral gland
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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
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how is urine formed in human
Rahma
what is the diference between a cavity and a canal
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what is the causative agent of malaria
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malaria is caused by an insect called mosquito.
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Malaria is cause by female anopheles mosquito
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Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
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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
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how are lungs work
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where does digestion begins
Achiri Reply
in the mouth
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what are the functions of follicle stimulating harmones?
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stimulates the follicle to release the mature ovum into the oviduct
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what are the functions of Endocrine and pituitary gland
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endocrine secrete hormone and regulate body process
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while pituitary gland is an example of endocrine system and it's found in the Brain
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Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
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biology is the study of life.
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Biology is the study of how living organisms live and survive in a specific environment
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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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