0
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 = 8
4x + 8y = 16
Solve the first equation for x:
x = 4 - 2y
Plug 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 = 8
4x + 8y = 15
Solve the first equation for x:
x = 4 - 2y
Plug 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.
Still curious? Ask our experts.
Chat with our AI personalities
Taiga
Lao
DevinAdd your answer:
Earn +20 pts
How many solutions does an consistent and dependent system of equations have?
It has more than one solutions.
What is the condition for unique solution of linear equation?
The equations are consistent and dependent with infinite solution if and only if a1 / a2 = b1 / b2 = c1 / c2.
What is dependent and inconsistent system?
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.
What makes an equation either inconsistent consistent dependent or independent?
That doesn't apply to "an" equation, but to a set of equations (2 or more). Two equations are:* Inconsistent, if they have no common solution (a set of values, for the variables, that satisfies ALL the equations in the set). * Consistent, if they do. * Dependent, if one equation can be derived from the others. In this case, this equation doesn't provide any extra information. As a simple example, one equation is the same as another equation, multiplying both sides by a constant. * Independent, if this is not the case.
What causes change in a dependent variable?
The dependent variable is dependent on the independent variable, so when the independent variable changes, so does the dependent variable.
