<< Chapter < Page Chapter >> Page >

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

Got questions? Get instant answers now!

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

Yes

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Yes

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

For the following exercises, solve each system by substitution.

   x + 3 y = 5 2 x + 3 y = 4

( −1 , 2 )

Got questions? Get instant answers now!

  3 x −2 y = 18 5 x + 10 y = −10

Got questions? Get instant answers now!

4 x + 2 y = −10 3 x + 9 y = 0

( −3 , 1 )

Got questions? Get instant answers now!

2 x + 4 y = −3.8 9 x −5 y = 1.3

Got questions? Get instant answers now!

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

( 3 5 , 0 )

Got questions? Get instant answers now!

    x −0.2 y = 1 −10 x + 2 y = 5

Got questions? Get instant answers now!

     3 x + 5 y = 9 30 x + 50 y = −90

No solutions exist.

Got questions? Get instant answers now!

  −3 x + y = 2 12 x −4 y = −8

Got questions? Get instant answers now!

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

( 72 5 , 132 5 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

For the following exercises, solve each system by addition.

−2 x + 5 y = −42    7 x + 2 y = 30

( 6 , −6 )

Got questions? Get instant answers now!

6 x −5 y = −34 2 x + 6 y = 4

Got questions? Get instant answers now!

     5 x y = −2.6 −4 x −6 y = 1.4

( 1 2 , 1 10 )

Got questions? Get instant answers now!

7 x −2 y = 3 4 x + 5 y = 3.25

Got questions? Get instant answers now!

  −x + 2 y = −1 5 x −10 y = 6

No solutions exist.

Got questions? Get instant answers now!

       7 x + 6 y = 2 −28 x −24 y = −8

Got questions? Get instant answers now!

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

( 1 5 , 2 3 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

( x , x + 3 2 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

5 x + 9 y = 16    x + 2 y = 4

( −4 , 4 )

Got questions? Get instant answers now!

6 x −8 y = −0.6 3 x + 2 y = 0.9

Got questions? Get instant answers now!

5 x −2 y = 2.25 7 x −4 y = 3

( 1 2 , 1 8 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

7 x −4 y = 7 6 2 x + 4 y = 1 3

( 1 6 , 0 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

( x , 2 ( 7 x −6 ) )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

( 5 6 , 4 3 )

Got questions? Get instant answers now!

  0.1 x + 0.2 y = 2 0.35 x −0.3 y = 0

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

x + 2 y = 4   2 x −4 y = 1

Got questions? Get instant answers now!

   x + 2 y = 7 2 x + 6 y = 12

Consistent with one solution

Got questions? Get instant answers now!

3 x −5 y = 7    x −2 y = 3

Got questions? Get instant answers now!

   3 x −2 y = 5 −9 x + 6 y = −15

Dependent with infinitely many solutions

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

( −3.08 , 4.91 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

( −1.52 , 2.29 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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 )

Got questions? Get instant answers now!

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

( −1 A B , A A B )

Got questions? Get instant answers now!

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 )

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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 )

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

Questions & Answers

find the sum of 28th term of the AP 3+10+17+---------
Prince Reply
I think you should say "28 terms" instead of "28th term"
Vedant
if sequence sn is a such that sn>0 for all n and lim sn=0than prove that lim (s1 s2............ sn) ke hole power n =n
SANDESH Reply
write down the polynomial function with root 1/3,2,-3 with solution
Gift Reply
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
Pream Reply
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Oroke Reply
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
kiruba Reply
what is the answer to dividing negative index
Morosi Reply
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
Shivam Reply
give me the waec 2019 questions
Aaron Reply
the polar co-ordinate of the point (-1, -1)
Sumit Reply
prove the identites sin x ( 1+ tan x )+ cos x ( 1+ cot x )= sec x + cosec x
Rockstar Reply
tanh`(x-iy) =A+iB, find A and B
Pankaj Reply
B=Ai-itan(hx-hiy)
Rukmini
Give me the reciprocal of even number
Aliyu
The reciprocal of an even number is a proper fraction
Jamilu
what is the addition of 101011 with 101010
Branded Reply
If those numbers are binary, it's 1010101. If they are base 10, it's 202021.
Jack
extra power 4 minus 5 x cube + 7 x square minus 5 x + 1 equal to zero
archana Reply
the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask