What is the difference between inconsistent and dependent

The x and y axes cross at a point referred to as the origin, where the coordinates are 0,0. If a consistent system has exactly one solution, it is independent. When the lines are parallel, there are no solutions, and sometimes the two equations will graph as the same line, in which case we have an infinite number of solutions. Some special terms are sometimes used to describe these kinds of systems. The following terms refer to how many solutions the system has.

We can also observe that the system is inconsistent by analyzing the graphs of each of the equations in the system. Notice that the two lines are parallel.

This makes sense, because the solution to a system of equations is where their graphs intersect. An equation can have infinitely many solutions when it should satisfy some conditions. In other words, when the two lines are the same line, then the system should have infinite solutions. It means that if the system of equations has an infinite number of solution, then the system is said to be consistent. In this page you can discover 68 synonyms, antonyms, idiomatic expressions, and related words for inconsistent, like: agree, variable, erratic, conflicting, unsteady, fantastical, continue, contradictory, discrepant, uncertain and same.

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. The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables. The dependent variable is the one that depends on the value of some other number.

Another way to put it is the dependent variable is the output value and the independent variable is the input value. Independent variable causes an effect on the dependent variable.

Example: How long you sleep independent variable affects your test score dependent variable. This makes sense, but: Example: Your test score affects how long you sleep. The dependent variable is the variable that is being measured or tested in an experiment. The dependent variable is dubbed dependent because it is thought to depend in some way on the variations of the independent variable.

Time is a common independent variable, as it will not be affeced by any dependent environemental inputs. Time can be treated as a controllable constant against which changes in a system can be measured. Varsity Tutors connects learners with experts. Instructors are independent contractors who tailor their services to each client, using their own style, methods and materials.

If a system has at least one solution, it is said to be consistent. Subjects Near Me. Download our free learning tools apps and test prep books. For linear equations in two variables, inconsistent systems have no solution, while dependent systems have infinitely many solutions. Explain when systems of equations in two variables are inconsistent or dependent both graphically and algebraically. A system of linear equations with no common solution because they represent parallel lines, which have no point or line in common.

A system of linear equations in which the two equations represent the same line; there are an infinite number of solutions to a dependent system. Recall that a linear system may behave in any one of three possible ways:. Also recall that each of these possibilities corresponds to a type of system of linear equations in two variables. An inconsistent system has no solution, and a dependent system has an infinite number of solutions. The previous modules have discussed how to find the solution for an independent system of equations.

We will now focus on identifying dependent and inconsistent systems of linear equations. The equations of a linear system are independent if none of the equations can be derived algebraically from the others. When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set.

Systems that are not independent are by definition dependent. Equations in a dependent system can be derived from one another; they describe the same line. They do not add new information about the variables, and the loss of an equation from a dependent system does not change the size of the solution set.