Linear system of equations and its solution(s)

No, because each line represents a unique equation and if two or more lines intersect at the same point, it means that those equations are all the same. Therefore, a system of linear equations cannot have multiple, finite solutions.In summary, a system of linear algebraic equations can have 1 solution, zero solutions, or infinite solutions. It cannot have multiple, finite solutions because this would mean that the equations are all the same, making the system dependent.
  • #1
fisico30
374
0
Hello Forum,

a system of linear algebraic equations can have 1 solution, zero solutions, or infinite solutions.

Can it ever have multiple, finite solutions? Why not?

when the system has infinite solutions, are the equations representing all the same identical equation, i.e. they are all dependent? Graphically, the solution space is a straight line...

thanks,
fisico30
 
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  • #2
fisico30 said:
Hello Forum,

a system of linear algebraic equations can have 1 solution, zero solutions, or infinite solutions.

Can it ever have multiple, finite solutions? Why not?

Graphically, a solution to a system of linear equations would be a point where all of the lines intersect. Can two or more lines intersect at a finite number of points?
 

FAQ: Linear system of equations and its solution(s)

What is a linear system of equations?

A linear system of equations is a set of two or more equations that contain two or more variables. The variables in each equation are related to each other in a linear fashion, meaning they can be expressed as a straight line when graphed.

How do you solve a linear system of equations?

There are several methods for solving a linear system of equations, including substitution, elimination, and graphing. The most common method is using elimination, where you manipulate the equations to eliminate one variable and solve for the remaining variable.

What is a solution to a linear system of equations?

A solution to a linear system of equations is a set of values for the variables that make all of the equations true. In other words, it is the point or points where the equations intersect on a graph.

Can a linear system of equations have more than one solution?

Yes, a linear system of equations can have one, infinite, or no solutions. If the equations are consistent and intersect at one point, there is one solution. If the equations are consistent and intersect at every point, there are infinite solutions. If the equations are inconsistent and do not intersect, there are no solutions.

What is the importance of solving a linear system of equations?

Solving a linear system of equations is essential in many mathematical and scientific applications. It allows us to find the relationships between variables and determine the values of unknown quantities. It is also a fundamental concept in algebra and serves as a basis for more complex mathematical concepts.

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