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- 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.
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Practice set b
Slove the system
Substitution produces
or
, a contradiction. These lines are parallel and the system is inconsistent.
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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.
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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
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Practice set d
Exercises
For the following problems, solve the systems by substitution.
Exercises for review
Questions & Answers
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Step 2: Find each score's deviation from the mean. ...
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Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits
Akshay
Sorry i want to learn more about this question
Bright
a= 0.20233
b=0.3384
Sufiyan
How do I interpret level of significance?
It depends on your business problem or in Machine Learning you could use ROC- AUC cruve to decide the threshold value
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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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