<< Chapter < Page Chapter >> Page >

Does the generic solution to a dependent system always have to be written in terms of x ?

No, you can write the generic solution in terms of any of the variables, but it is common to write it in terms of x and if needed x and y .

Solve the following system.

     x + y + z = 7 3 x 2 y z = 4 x + 6 y + 5 z = 24

Infinite number of solutions of the form ( x , 4 x −11 , −5 x + 18 ) .

Got questions? Get instant answers now!

Access these online resources for additional instruction and practice with systems of equations in three variables.

Key concepts

  • A solution set is an ordered triple { ( x , y , z ) } that represents the intersection of three planes in space. See
    [link] .
  • A system of three equations in three variables can be solved by using a series of steps that forces a variable to be eliminated. The steps include interchanging the order of equations, multiplying both sides of an equation by a nonzero constant, and adding a nonzero multiple of one equation to another equation. See [link] .
  • Systems of three equations in three variables are useful for solving many different types of real-world problems. See [link] .
  • A system of equations in three variables is inconsistent if no solution exists. After performing elimination operations, the result is a contradiction. See [link] .
  • Systems of equations in three variables that are inconsistent could result from three parallel planes, two parallel planes and one intersecting plane, or three planes that intersect the other two but not at the same location.
  • A system of equations in three variables is dependent if it has an infinite number of solutions. After performing elimination operations, the result is an identity. See [link] .
  • Systems of equations in three variables that are dependent could result from three identical planes, three planes intersecting at a line, or two identical planes that intersect the third on a line.

Section exercises

Verbal

Can a linear system of three equations have exactly two solutions? Explain why or why not

No, there can be only one, zero, or infinitely many solutions.

Got questions? Get instant answers now!

If a given ordered triple solves the system of equations, is that solution unique? If so, explain why. If not, give an example where it is not unique.

Got questions? Get instant answers now!

If a given ordered triple does not solve the system of equations, is there no solution? If so, explain why. If not, give an example.

Not necessarily. There could be zero, one, or infinitely many solutions. For example, ( 0 , 0 , 0 ) is not a solution to the system below, but that does not mean that it has no solution.

     2 x + 3 y −6 z = 1 −4 x −6 y + 12 z = −2        x + 2 y + 5 z = 10

Got questions? Get instant answers now!

Using the method of addition, is there only one way to solve the system?

Got questions? Get instant answers now!

Can you explain whether there can be only one method to solve a linear system of equations? If yes, give an example of such a system of equations. If not, explain why not.

Every system of equations can be solved graphically, by substitution, and by addition. However, systems of three equations become very complex to solve graphically so other methods are usually preferable.

Got questions? Get instant answers now!

Questions & Answers

it is the relatively stable flow of income
Chidubem Reply
what is circular flow of income
Divine Reply
branches of macroeconomics
SHEDRACK Reply
what is Flexible exchang rate?
poudel Reply
is gdp a reliable measurement of wealth
Atega Reply
introduction to econometrics
Husseini Reply
Hi
mostafa
hi
LEMLEM
hello
Sammol
hi
Mahesh
bi
Ruqayat
hi
Ruqayat
Hi fellas
Nyawa
hey
Sammol
hi
God
hello
Jahara
Good morning
Jorge
hi
abubakar
hi
Nmesoma
hi
Mahesh
Hi
Tom
Why is unemployment rate never zero at full employment?
Priyanka Reply
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
Rushawn Reply
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost 6% more than previous year? Provide with reasoning.
Geetha Reply
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
Alii Reply
what is the problem of macroeconomics
Yoal
Economic growth Stable prices and low unemployment
Ephraim
explain inflationcause and itis degre
Miresa Reply
what is inflation
Getu
increase in general price levels
WEETO
Good day How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200. Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
Chisomo Reply
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
Thapase Reply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
Mercy Reply
Hi
Isiaka
Hi
Geli
hy
Man
👋
Bahunda
hy how are you?
Man
ys
Amisha
how are you guys
Sekou
f9 guys
Amisha
how are you guys
Sekou
ys am also fine
Amisha
fine and you guys
Geli
from Nepal
Amisha
nawalparasi district from belatari
Amisha
nd u
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9 no Mpc is greater than 1 Y=100+.9Y+50 Y-.9Y=150 0.1Y/0.1=150/0.1 Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output? discuss your answer using appropriate graph.
Galge Reply
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 1

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




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