Why Does a Linear System Have a Single Solution?

[nhrock3]

why lenear system has a single solution?

 

[Mark44]

In general, a linear system of equations can have no solution, a single solution, or an infinite number of solutions. Do you have a question about a particular linear system?

 

[nhrock3]

it for electrical circuit theory

for thevenin theorem

i have a pi system which has independent sources

and my prof said

"we have a lenear system so the is a single solution"

i can't understand why?

 

[Mark44]

I don't know what a "pi system" is. In any case, unless you know something about the linear system, you can't tell how many solutions it has.

Here are three very simple examples:

1. No solutions
x + 2y = 3
x + 2y = 4

2. Exactly one solution
x + y = 3
x - y = 1
(solution is x = 2, y = 1)

3. Infinite number of solutions
x + y = 3
2x + 2y = 6

 

[HallsofIvy]

Note Mark44's options: one solution, no solution, infinite number of solutions.

If you know the problem has a non-zero finite number of solutions then you can say there is a single solution- as opposed to, say, a quadratic equation in which there can be two solutions.