Math and Arithmetic
Linear Algebra

# What are the three types of system of linear equations?

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###### 2015-12-28 20:31:03

The three types are

• the system has a unique solution
• the system has no solutions
• the system has infinitely many solutions.
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## Related Questions

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

A system of equations can be solved using subtraction, addition, multiplication, and substitution.https://www.wikihow.com/Solve-Systems-of-Equations

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.

There is only one type of solution if there are two linear equations. and that is the point of intersection listed in (x,y) form.

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Generally, both types of equation contain an equals sign and some combination of numbers and/or variables. That is the only thing I can think of that is common between all types of nonlinear and linear equations.

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There are various processes:Trial and error. It can sometimes work. Not recommended, but it can work sometimes, particularly if there are external factors that suggest values for some of the variables.Plotting the lines represented by the equations to find their point(s) of intersection. Good for two variables, just about feasible with three but not sensible for more variables.Substitution involves using one equation to express one of the variables in terms of the others. The next step is to substitute for that variable in the remaining equations. Repeat the process and, step-by-step, reduce the number of variables and equations to one. Solve that equation and then work back. Elimination is an equivalent method and uses linear combinations of the equations to eliminate one variable at a time from the system of equations so as to arrive at a single equation in one variable. Suppose the system of n equations in n variables is represented in matrix form by Ax = y where A is the nxn matrix of coefficients of the equations, and x is an m*1 column vector of variables and y is a m*1 vector of constants. Then the solution (if it exists) is A-1y, where A-1 is the inverse matrix of A.

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