What is consistent and inconsistent with example?

A system of linear equations is a group of two or more linear equations having the same variables. For example, x + 2y = 14 , 2x + y = 6. If there is nothing common between the two equations then it can be called inconsistent. But it will be called consistent if anyone ordered pair can solve both the equations.

What are consistent inconsistent and dependent equations?

If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent .

What is an example of an inconsistent system?

In other words, no two numbers exist such that 5 times the first number added to 2 gives the second number, and if you subtract 2 times the second number from 10 times the first number, you get 12. Zero can’t equal 16, so the statement 0 = 16 makes no sense. Therefore, the system is inconsistent and has no solution.

What is consistent and inconsistent system?

A consistent system of equations has at least one solution, and an inconsistent system has no solution.

What is the formula of inconsistent?

Inconsistent equations is defined as two or more equations that are impossible to solve based on using one set of values for the variables. An example of a set of inconsistent equations is x+2=4 and x+2=6. noun.

What is inconsistent and dependent?

A system of equations is called an inconsistent system of equations if there is no solution because the lines are parallel. A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions.

Are parallel lines consistent or inconsistent?

Parallel lines never intersect, so they have no solutions. Since the lines are parallel, it is an inconsistent system.

What is a Dependant system?

A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions. These two situations occur when trying to solve for a system of equations. First a system of equations is called Inconsistent if there is no solution because the lines are parallel.

How many solutions does a dependent system have?

infinite solutions
A dependent system of equations has infinite solutions, and an independent system has a single solution.

What is the solution set to an inconsistent system of equations?

A solution set is the set of all the intersection points of the equations in the system. A solution set can have a finite number of solutions, an infinite number of solutions, or no solution. When the system has no solution, we say that the system is inconsistent.

What’s is consistent independent system of equations?

Systems of equations can be classified by the number of solutions. If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent .

What is consistent and dependent?

A set of equations is consistent and independent if they have only one intersection. A set of equations is consistent and dependent if they are the same line. A set of equations is inconsistent if they do not have a point of intersection. Now we want to see if there are any points of intersection.

What is the definition of consistent system?

A Consistent System of Equations. A consistent system of equations is a system that has at least one solution. An inconsistent system of equations is a system that has no solution. Thus, of the three possibilities for solutions of a system, we see that the first two possibilities represent consistent systems because they have at least one solution,…

What is consistent system of linear equations?

a linear or nonlinear system of equations is consistent if there is at least one set of values for the unknowns that satisfies every equation in the system—that is, that when substituted into each of the equations makes the equation hold true as an identity.