How do you know if an equation is consistent or independent?

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 .

What is an example of consistent independent?

A consistent system is considered to be an independent system if it has a single solution, such as the example we just explored. The two lines have different slopes and intersect at one point in the plane.

What is an example of a consistent equation?

Consistent systems have at least one solution in common. For example, the equations x + y = 6 and x – y = 2 have one solution in common, the ordered pair (4, 2) because 4 + 2 equals 6 and 4 – 2 equals 2.

What is an example of an independent equation?

The equations 3x + 2y = 6 and 3x + 2y = 12 are independent, because any constant times one of them fails to produce the other one.

How do you find the consistency of an equation?

i) If both the lines intersect at a point, then there exists a unique solution to the pair of linear equations. In such a case, the pair of linear equations is said to be consistent.

What is a consistent independent?

Consistent Independent: A system of linear equations is consistent independent when it has exactly one solution. When this is the case, the graphs of the lines in the system cross at exactly one point. Inconsistent: A system of linear equations is inconsistent if it has no solutions.

How do you find the inconsistent equation?

To see if the pair of linear equations is consistent or inconsistent, we try to gain values for x and y. If both x and y have the same value, the system is consistent. The system becomes inconsistent when there are no x and y values that satisfy both equations.

What is independent Math?

An independent variable is a variable that represents a quantity that is being manipulated in an experiment. x is often the variable used to represent the independent variable in an equation.

What is consistent and independent?

Definitions: If the two equations describe lines that intersect once, the system is independent and consistent. If the two equations describe parallel lines, and thus lines that do not intersect, the system is independent and inconsistent.

What is a inconsistent equation in math?

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.