Linear system of equations and its solution(s)

[fisico30]

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

 

[eumyang]

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?