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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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ex 2.1 question no 11
khansa
anyone can help me
khansa
ex 2.1 question no. 11
khansa
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any genius online ? I need help!!
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plz help me in question
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evaluate the following computation (x³-8/x-2)
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teach me also how to solve the first law of calculus
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only god knows😂
abdulkadir
f(x) = x-2
g(x) = 3x + 5
fog(x)?
f(x)/g(x)
fog(x)= f(g(x))
= x-2
= 3x+5-2
= 3x+3
f(x)/g(x)= x-2/3x+5
diron
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(mathematics) For a complex number a+bi, the principal square root of the sum of the squares of its real and imaginary parts, √a2+b2 . Denoted by | |.
The absolute value |x| of a real number x is √x2 , which is equal to x if x is non-negative, and −x if x is negative.
Ismael
find integration of loge x
find the volume of a solid about the y-axis, x=0, x=1, y=0, y=7+x^3
Can calculus give the answers as same as other methods give in basic classes while solving the numericals?
y=(x^2 + 3x).(eipix)
Claudia
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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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