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
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
