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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.

Q: What is consistent and dependent?

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It has more than one solutions.

The equations are consistent and dependent with infinite solution if and only if a1 / a2 = b1 / b2 = c1 / c2.

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.

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.

The dependent variable is dependent on the independent variable, so when the independent variable changes, so does the dependent variable.

Related questions

The three types of linear equations are: Consistent Dependent, Consistent Independent, and Inconsistent.

consistent dependent

It has more than one solutions.

The equations are consistent and dependent with infinite solution if and only if a1 / a2 = b1 / b2 = c1 / c2.

Scientists use controlled experiments because the results are consistent and can be replicated. The control of an experiment is the value that you are controlling the dependent variable to.

Scientists use controlled experiments because the results are consistent and can be replicated. The control of an experiment is the value that you are controlling the dependent variable to.

Swing is a library of GUI controls. Classes in swing are not OS dependent. They do not take the look and feel of the target platform so that they have a consistent appearance.

Wave energy is not always available as it is dependent on the presence of waves. Factors such as weather conditions and location play a role in the consistent availability of wave energy. However, in areas with consistent wave patterns, wave energy can be a reliable source of renewable energy.

The factors in an experiment that remain constant are called control variables. These are kept consistent to ensure that any changes observed in the dependent variable are due to the manipulation of the independent variable and not influenced by outside factors. Control variables help to isolate the effect of the independent variable on the dependent variable.

analytical method is the easiest way to determine if it is consistent,inconsistent,or dependent.I will show you how it is done.let say:4x+5y=108x+10y=20are they dependent, independent , or inconsistent.dependent:A=B=C the dependent are all equal.independent or consistent:A / B / C the consistent are not equal to each other.inconsistent:A=B / C the inconsistent is A is equal to B and B is NOTequal to C.1.)you must get the numerical coefficient of the numbers4 =5=108 10 202.) simplify1 = 1 = 12 2 2 they are all equal so they are called dependent variable.thx!!!!

The brain receives about 20% of the body's oxygen supply. It is a highly oxygen-dependent organ, requiring a consistent supply of oxygen to function properly.

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.