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- Elementary algebra
- 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
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Omeprazole
Cimetidine / Tagament
For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
how does the stomach protect itself from the damaging effects of HCl
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
function of digestive
Ali
what is the normal body temperature
please why 37 degree selcius normal temperature
Mark
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
how does Lysin attack pathogens
Diya
I information on anatomy position and digestive system and there enzyme
anatomy of the female external genitalia
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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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