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
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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