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Suppose we have two linear equations in two unknowns. If the equations are plotted on a rectangular grid, the graph will fit one of these scenarios:
1) The two lines cross each other (intersect).
2) The two lines don't cross - they are parallel lines
3) The two lines fall on top of each other - they're really the same line.
In case 3) the two lines are dependent - one can be changed into the other. In cases 1) and 2) we say the lines are independent.
If the pair of equations has a solution (one or more points in common) we say they are consistent ... cases 1) and 3). In case 2) the system is inconsistent; there is no solution.
To summarize:
1) Intersecting lines are consistent and independent.
2) Parallel lines are inconsistent and independent.
3) Coincident ["happen together"] lines are consistent and dependent.
*** A second order linear system CANNOT be both dependent and inconsistent.
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How can you identify a dependent or inconsistent system by looking at an augmented matrix in reduced row-echelon form?
And your question is......................?
What do both dependent and inconsistent systems have in common?
no solution
What describes a system of equations that has no solution?
Inconsistent.
When will a system of linear equations be inconsistent?
When the matrix of coefficients is singular.
What is consistent and dependent?
The terms consistent and dependent are two ways to describe a system of linear equations. A system of linear equations is dependent if you can algebraically derive one of the equations from one or more of the other equations. A system of linear equations is consistent if they have a common solution.An example of a dependent system of linear equations:2x + 4y = 84x + 8y = 16Solve the first equation for x:x = 4 - 2yPlug that value of x into the second equation:16 - 8y + 8y = 16, which gives 16 = 16.No new information was gained from the second equation, because we already knew 16 = 16, so these two equations are dependent.An example of an inconsistent system of linear equations:Because consistency is boring.2x + 4y = 84x + 8y = 15Solve the first equation for x:x = 4 - 2yPlug that value of x into the second equation:16 - 8y + 8y = 15, which gives 16 = 15.This is a contradiction, because 16 doesn't equal 15. Therefore this system has no solution and is inconsistent.
What happens when Cramer's rule is applied to dependent or inconsistent systems?
We call the coefficients of the variables in the system D, and we need to find the determinant of D. When D = 0, the system is either inconsistent or dependent. You need another method to solve it.
How can you identify a dependent or inconsistent system by looking at an augmented matrix in reduced row-echelon form?
And your question is......................?
How many solutions does an independent system have?
an independent system only has one solution, a dependent has many or an infinite number and an inconsistent system has 0 because the line are parelle
How can you identify a dependent or inconsistent system by looking at an augmented matrix in reduced row echelon form?
I bet it can be done, but I'll be darned if I can!
How many solutions does an inconsistent system of equations have?
If a system is inconsistent it cannot have any solutions.A system of equations is considered inconsistent when the lines are parallel which means they never intersect so there are no solutions.A system is considered consistent when they intersect at one point and have one solution (Also known as an independent system of equations).Dependent Systems are when the lines coincide (the same equation) so they have an infinite number of solutions.
What do both dependent and inconsistent systems have in common?
no solution
How many solutions does an inconsistent system have?
How many solutions does an inconsistent system have
What is a inconsistent system?
An inconsistent system of equations is when you have 2 or more equations, but it is not possible to satisfy all of them at the same time. (E.g if you have 3 equations, but can only satisfy 2 at once, it is an inconsistent system).
If a system has no solution what type of system is this?
It is an inconsistent system.
If a system has no solutions what type of system is this?
inconsistent
How many solutions does an inconsistent equation have?
An inconsistent equation (or system of equations) is one that has no possible solutions. That is precisely why we call it inconsistent; there is no solution set that can be substituted for its variable or variables that will make the equation (or system) true.
What describes a system of equations that has no solution?
Inconsistent.
