Best Answer

Independence:

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.

Consistency:

The equations of a linear system are consistent if they possess a common solution, and inconsistent otherwise. When the equations are inconsistent, it is possible to derive a contradiction from the equations, such as the statement that 0 = 1.

Homogeneous:

If the linear equations in a given system have a value of zero for all of their constant terms, the system is homogeneous.If one or more of the system's constant terms aren't zero, then the system is nonhomogeneous.

Study guides

☆☆

Q: What are the three types of systems of linear equations and their characteristics?

Write your answer...

Submit

Still have questions?

Related questions

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

1

There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.

A linear equation is one degree equation. It will be in one , two and three variables. Nonlinear equations have degree other than one.

Systems of linear equations are simply two or more linear equations related to each other, whether it be through having similar variables or describing similar processes.Linear equations are equations whose only terms are constants and/or single variables raised to the first power. More than one variable is allowed in a linear equation, but it is not allowed to be multiplied with another variable. Constants are allowed to be multiplied to variables in linear equations. These equations are called "linear" due to the fact that their solution set forms a line when represented in classic Euclidean space, e.g. when graphed on the mutually perpendicular x, y, and z axes of the Cartesian coordinate system.Some examples of linear equations are as follows:x+2 = 3x+y+z = 42*a+3*b+4*c+5*d = 10*eIf these three linear equations were all necessary to describe something mathematically, they would be a system of linear equations.To solve a system of linear equations for every unknown, the number of variables must be less than or equal to the number of equations.To actually solve systems of linear equations, the easiest way is to use a calculator and linear algebra.If you had something like this:{ 2*x+3*y = 5{ 4*x+10*y = 7What you would do is this:1. Put the coefficients in a matrix:[2 3][4 10]2. Now put the answers in a matrix:[5][7]3. Invert the matrix of the coefficients and multiply that by the answer:[2 3] ^(-1) = [1.25 -.375][4 10] [-.5 .25]4. Multiply this by the matrix[5][7][1.25 -.375] * [5][-.5 .25] [7]=[3.625][-0.75]Meaning your x = 3.625 and your y = -.75

There are no disadvantages. There are three main ways to solve linear equations which are: substitution, graphing, and elimination. The method that is most appropriate can be found by looking at the equation.

Single answer. Coincidental (same equation), No solution.

The three types arethe system has a unique solutionthe system has no solutionsthe system has infinitely many solutions.

There is no simple answer. Sometimes, the nature of one of the equations lends itself to the substitution method but at other times, elimination is better. If they are non-linear equations, and there is an easy substitution then that is the best approach. With linear equations, using the inverse matrix is the fastest method.

There are several methods to do this; the basic idea is to reduce, for example, a system of three equations with three variables, to two equations with two variables. Then repeat, until you have only one equation with one variable. Assuming only two variables, for simplicity: One method is to solve one of the equations for one of the variables, then replace in the other equation. Another is to multiply one of the equations by some constant, the other equation by another constant, then adding the resulting equations together. The constants are chosen so that one of the variables disappear. Specifically for linear equations, there are various advanced methods based on matrixes and determinants.

Three different kinds: none, one and infinitely many.

"Linear" equations are simply those where the highest power of any variable is 1 (one). There could be 2 variables in which case it is a straight line, or there might be three in which case it is a flat plane, or there might be a million in which case we don't know what it actually looks like.

People also asked