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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
it is the relatively stable flow of income
what is circular flow of income
branches of macroeconomics
what is Flexible exchang rate?
is gdp a reliable measurement of wealth
introduction to econometrics
Why is unemployment rate never zero at full employment?
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
what is the problem of macroeconomics
Yoal
Economic growth
Stable prices
and low unemployment
Ephraim
explain inflationcause and itis degre
increase in general price levels
WEETO
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
nawalparasi district
from belatari
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
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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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