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- Systems of linear equations
- Elimination by addition
Practice set a
Solve each system by addition.
Sample set b
Solve the following systems using the addition method.
Solve
Step 1: The equations are already in the proper form,
Step 2: If we multiply equation (2) by —3, the coefficients of
will be opposites and become 0 upon addition, thus eliminating
.
Step 3: Add the equations.
Step 4: Solve the equation
Step 5: Substitute
into either of the original equations. We will use equation 2.
We now have
and
Step 6: Substitute
and
into both the original equations for a check.
Step 7: The solution is
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Solve
Step 1: Rewrite the system in the proper form.
Step 2: Since the coefficients of
already have opposite signs, we will eliminate
.
Multiply equation (1) by 5, the coefficient of
in equation 2.
Multiply equation (2) by 2, the coefficient of
in equation 1.
Step 3: Add the equations.
Step 4: Solve the equation
Step 5: Substitute
into either of the original equations. We will use equation 1.
We now have
and
Step 6: Substitution will show that these values check.
Step 7: The solution is
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Practice set b
Solve each of the following systems using the addition method.
Addition and parallel or coincident lines
When the lines of a system are parallel or coincident, the method of elimination produces results identical to that of the method of elimination by substitution.
Addition and parallel lines
If computations eliminate all variables and produce a contradiction, the two lines of the system are parallel and the system is called inconsistent.
Addition and coincident lines
If computations eliminate all variables and produce an identity, the two lines of the system are coincident and the system is called dependent.
Sample set c
Solve
Step 1: The equations are in the proper form.
Step 2: We can eliminate
by multiplying equation (1) by –2.
Step 3: Add the equations.
This is false and is therefore a contradiction. The lines of this system are parallel. This system is inconsistent.
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Solve
Step 1: The equations are in the proper form.
Step 2: We can eliminate
by multiplying equation (1) by –3 and equation (2) by 4.
Step 3: Add the equations.
This is true and is an identity. The lines of this system are coincident.
This system is dependent.
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Practice set c
Solve each of the following systems using the addition method.
Exercises
For the following problems, solve the systems using elimination by addition.
Exercises for review
Questions & Answers
how does Neisseria cause meningitis
is the branch of biology that deals with the study of microorganisms.
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
How bacteria create energy to survive?
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
which site have a normal flora
Many sites of the body have it
Skin
Nasal cavity
Oral cavity
Gastro intestinal tract
Safaa
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
part of a tissue or an organ being wounded or bruised.
Wilfred
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Source:
OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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