-
Home
- Elementary algebra
- Systems of linear equations
- Elimination by substitution
Substitution and parallel lines
If computations eliminate all the variables and produce a contradiction, the two lines of a system are parallel, and the system is called inconsistent.
Sample set b
Solve the system
Step 1: Solve equation 1 for
Step 2: Substitute the expression
for
into equation 2.
Step 3: Solve the equation obtained in step 2.
Computations have eliminated all the variables and produce a contradiction. These lines are parallel.
This system is inconsistent.
Got questions? Get instant answers now!
Practice set b
Slove the system
Substitution produces
or
, a contradiction. These lines are parallel and the system is inconsistent.
Got questions? Get instant answers now!
Substitution and coincident lines
The following rule alerts us to the fact that the two lines of a system are coincident.
Substitution and coincident lines
If computations eliminate all the variables and produce an identity, the two lines of a system are coincident and the system is called dependent.
Sample set c
Solve the system
Step 1: Divide equation 1 by 4 and solve for
Step 2: Substitute the expression
for
in equation 2.
Step 3: Solve the equation obtained in step 2.
Computations have eliminated all the variables and produced an identity. These lines are coincident.
This system is dependent.
Got questions? Get instant answers now!
Practice set c
Systems in which a coefficient of one of the variables is not 1 or cannot be made to be 1 without introducing fractions are not well suited for the substitution method. The problem in Sample Set D illustrates this “messy” situation.
Sample set d
Solve the system
Step 1: We will solve equation
for
Step 2: Substitute the expression
for
in equation
Step 3: Solve the equation obtained in step 2.
Step 4: Substitute
into the equation obtained in step
We now have
and
Step 5: Substitution will show that these values of
and
check.
Step 6: The solution is
Got questions? Get instant answers now!
Practice set d
Exercises
For the following problems, solve the systems by substitution.
Exercises for review
Questions & Answers
how to create a software using Android phone
what is the difference between C and C++.
software is a instructions like programs
Shambhu
what is the difference between C and C++.
Yan
what is software engineering
Ahmad
software engineering is a the branch of computer science deals with the design,development, testing and maintenance of software applications.
Hayder
who is best bw software engineering and cyber security
Ahmad
Both software engineering and cybersecurity offer exciting career prospects, but your choice ultimately depends on your interests and skills. If you enjoy problem-solving, programming, and designing software syste
Hayder
what's software processes
I haven't started reading yet. by device (hardware) or for improving design Lol? Here. Requirement, Design, Implementation, Verification, Maintenance.
Vernon
I can give you a more valid answer by 5:00 By the way gm.
Vernon
it is all about designing,developing, testing, implementing and maintaining of software systems.
Ehenew
hello assalamualaikum
Sami
My name M Sami I m 2nd year student
Sami
what is the specific IDE for flutter programs?
jegudgdtgd my Name my Name is M and I have been talking about iey my papa john's university of washington post I tagged I will be in
Show the necessary steps with description in resource monitoring process (CPU,memory,disk and network)
What is software engineering
Software engineering is a branch of computer science directed to writing programs to develop Softwares that can drive or enable the functionality of some hardwares like phone , automobile and others
kelvin
if any requirement engineer is gathering requirements from client and after getting he/she Analyze them this process is called
The following text is encoded in base 64.
Ik5ldmVyIHRydXN0IGEgY29tcHV0ZXIgeW91IGNhbid0IHRocm93IG91dCBhIHdpbmRvdyIgLSBTdGV2ZSBXb3puaWFr
Decode it, and paste the decoded text here
what to do you mean
Vincent
What is the command to list the contents of a directory in Unix and Unix-like operating systems
how can i make my own software free of cost
The name of the author of our software engineering book is Ian Sommerville.
the set of intruction given to the computer to perform a task
Noor
Got questions? Join the online conversation and get instant answers!
Source:
OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
Google Play and the Google Play logo are trademarks of Google Inc.