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.
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
