Another type of system of linear equations is an
inconsistent system , which is one in which the equations represent two parallel lines. The lines have the same slope and different
y- intercepts. There are no points common to both lines; hence, there is no solution to the system.
Types of linear systems
There are three types of systems of linear equations in two variables, and three types of solutions.
An
independent system has exactly one solution pair
The point where the two lines intersect is the only solution.
An
inconsistent system has no solution. Notice that the two lines are parallel and will never intersect.
A
dependent system has infinitely many solutions. The lines are coincident. They are the same line, so every coordinate pair on the line is a solution to both equations.
[link] compares graphical representations of each type of system.
Given a system of linear equations and an ordered pair, determine whether the ordered pair is a solution.
Substitute the ordered pair into each equation in the system.
Determine whether true statements result from the substitution in both equations; if so, the ordered pair is a solution.
Determining whether an ordered pair is a solution to a system of equations
Determine whether the ordered pair
is a solution to the given system of equations.
Substitute the ordered pair
into both equations.
The ordered pair
satisfies both equations, so it is the solution to the system.
There are multiple methods of solving systems of linear equations. For a
system of linear equations in two variables, we can determine both the type of system and the solution by graphing the system of equations on the same set of axes.
Solving a system of equations in two variables by graphing
Solve the following system of equations by graphing. Identify the type of system.
Solve the first equation for
Solve the second equation for
Graph both equations on the same set of axes as in
[link] .
The lines appear to intersect at the point
We can check to make sure that this is the solution to the system by substituting the ordered pair into both equations.
The solution to the system is the ordered pair
so the system is independent.
Can graphing be used if the system is inconsistent or dependent?
Yes, in both cases we can still graph the system to determine the type of system and solution. If the two lines are parallel, the system has no solution and is inconsistent. If the two lines are identical, the system has infinite solutions and is a dependent system.
Questions & Answers
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
