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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
(Pcos∅+qsin∅)/(pcos∅-psin∅)
how to answer the activity
how to solve the activity
Chabelita
solve for X,,4^X-6(2^)-16=0
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t he silly nut company makes two mixtures of nuts: mixture a and mixture b. a pound of mixture a contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for $4. a pound of mixture b contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for $5. the company has 1080
If
, ,
are the roots of the equation
3 2 0,
x px qx r
Find the value of
1
.
Parts of a pole were painted red, blue and yellow. 3/5 of the pole was red and 7/8 was painted blue. What part was painted yellow?
Parts of the pole was painted red, blue and yellow. 3 /5 of the pole was red and 7 /8 was painted blue. What part was painted yellow?
Patrick
how I can simplify algebraic expressions
Lairene and Mae are joking that their combined ages equal Sam’s age. If Lairene is twice Mae’s age and Sam is 69 yrs old, what are Lairene’s and Mae’s ages?
lairenea's age is 23yrs
ACKA
Laurene is 46 yrs and Mae is 23 is
Solomon
age does not matter
christopher
solve for X, 4^x-6(2*)-16=0
Alieu
prove`x^3-3x-2cosA=0
(-π<A<=π
create a lesson plan about this lesson
Excusme but what are you wrot?
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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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