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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

(1+cosA)(1-cosA)=sin^2A
BINCY Reply
good
Neha
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Mirza
Teach me abt the echelon method
Khamis
exact value of cos(π/3-π/4)
Ankit Reply
What is differentiation?
Intakhab Reply
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Thamarai Reply
(1+cosA)(1-cosA)=sin^2A
BINCY
differentiate f(t)=1/4t to the power 4 +8
Jessica Reply
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duru Reply
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Augustine
Why is 7 on top
Bertha Reply
simplify cot x / csc x
Catherine Reply
👉🌹Solve🌻 Given that: cotx/cosx =cosx/sinx/cosx =1/sinx =cosecx Ans.
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SIYAMTHEMBA Reply
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Patrick
simplify: cot x/csc x
Catherine
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Catherine
some to dereve formula for bulky density
kurash
Solve Given that: cotx/cosx =cosx/sinx/cosx =1/sinx =cosecx Ans.
Vijay
if tan alpha + beta is equal to sin x + Y then prove that X square + Y square - 2 I got hyperbole 2 Beta + 1 is equal to zero
Rahul Reply
questions
Thamarai
ok
AjA
sin^4+sin^2=1, prove that tan^2-tan^4+1=0
SAYANTANI Reply
what is the formula used for this question? "Jamal wants to save $54,000 for a down payment on a home. How much will he need to invest in an account with 8.2% APR, compounding daily, in order to reach his goal in 5 years?"
Kuz Reply
i don't need help solving it I just need a memory jogger please.
Kuz
A = P(1 + r/n) ^rt
Dale
how to solve an expression when equal to zero
Mintah Reply
its a very simple
Kavita
gave your expression then i solve
Kavita
Hy guys, I have a problem when it comes on solving equations and expressions, can you help me 😭😭
Thuli
Tomorrow its an revision on factorising and Simplifying...
Thuli
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kurash
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Kavita
Hi
Masum
What is the value of log-1
Masum
the value of log1=0
Kavita
Log(-1)
Masum
What is the value of i^i
Masum
log -1 is 1.36
kurash
No
Masum
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Kavita
No sister.
Masum
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Kavita
tan20°×tan30°×tan45°×tan50°×tan60°×tan70°
Joju Reply
jaldi batao
Joju
Find the value of x between 0degree and 360 degree which satisfy the equation 3sinx =tanx
musah Reply

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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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