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- Elementary algebra
- Systems of linear equations
- Summary of key concepts
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
Beginning with the graphical solution of systems, this chapter includes an interpretation of independent, inconsistent, and dependent systems and examples to illustrate the applications for these systems. The substitution method and the addition method of solving a system by elimination are explained, noting when to use each method. The five-step method is again used to illustrate the solutions of value and rate problems (coin and mixture problems), using drawings that correspond to the actual situation.This module presents a summary of the key concepts of the chapter "Systems of Linear Equations".
Summary of key concepts
System of equations (
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A collection of two linear equations in two variables is called a
system of equations.
Solution to a system (
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An ordered pair that is a solution to both equations in a system is called a
solution to the system of equations. The values
are a solution to the system
Independent systems (
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Systems in which the lines intersect at precisely one point are
independent systems. In applications, independent systems can arise when the collected data are accurate and complete.
Inconsistent systems (
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Systems in which the lines are parallel are
inconsistent systems. In applications, inconsistent systems can arise when the collected data are contradictory.
Dependent systems (
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Systems in which the lines are coincident (one on the other) are
dependent systems. In applications, dependent systems can arise when the collected data are incomplete.
Solving a system by graphing (
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To solve a system by graphing:
- Graph each equation of the same set of axes.
- If the lines intersect, the solution is the point of intersection.
Solving a system by substitution (
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To solve a system using substitution,
- Solve one of the equations for one of the variables.
- Substitute the expression for the variable chosen in step 1 into the other equation.
- Solve the resulting equation in one variable.
- Substitute the value obtained in step 3 into the equation obtained in step 1 and solve to obtain the value of the other variable.
- Check the solution in both equations.
- Write the solution as an ordered pair.
Solving a system by addition (
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To solve a system using addition,
- Write, if necessary, both equations in general form
- If necessary, multiply one or both equations by factors that will produce opposite coefficients for one of the variables.
- Add the equations to eliminate one equation and one variable.
- Solve the equation obtained in step 3.
- Substitute the value obtained in step 4 into either of the original equations and solve to obtain the value of the other variable.
- Check the solution in both equations.
- Write the solution as an ordered pair.
Substitution and addition and parallel lines (
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If computations eliminate all variables and produce a contradiction, the two lines of the system are parallel and no solution exists. The system is inconsistent.
Substitution and addition and coincident lines (
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If computations eliminate all variables and produce an identity, the two lines of the system are coincident and the system has infinitely many solutions. The system is dependent.
Applications (
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The five-step method can be used to solve applied problems that involve linear systems that consist of two equations in two variables. The solutions of number problems, mixture problems, and value and rate problems are examined in this section. The rate problems have particular use in chemistry.
Questions & Answers
what does preconceived mean
How can I develope my cognitive domain
why is communication effective
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
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miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
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Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
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ARC
A child is a member of community not society elucidate ?
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
compare and contrast skinner's perspective on personality development on freud
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
interpersonal relationships
What would be the best educational aid(s) for gifted kids/savants?
treat them normal, if they want help then give them.
that will make everyone happy
Saurabh
What are the treatment for autism?
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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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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