A system of 2 linear equations can have exactly 2 solutions true or false?

Question

anonymous · Answer

true

anonymous · Answer

x & y = two solutions

anonymous · Answer

I think the answer is false, because as I know any of n linear system equations have only one solution, no solution, or infinitely many solutions.

anonymous · Answer

It may have no solutions if the lines have same  slope, are parallel. So, false. "Can have" does not work well with "exactly."

anonymous · Answer

but his question wasnt asking how many solutions. it was asking if it can have exactly 2 solutions and therefore yes , it can.

loser66 · Answer

@wendylisette  the question is TRUE or FALSE

anonymous · Answer

exactly , so its true

anonymous · Answer

im agreeing with youu ..

ranga · Answer

I don't think x and y are counted as two different solutions.  It is one set of solutions.
Sp two linear equations can have one set of unique solution or no solutions at all or infinite number of solutions.  It cannot have EXACTLY two solutions.

e.mccormick · Answer

What ranga is talking about is the standard way it is viewed, where a solution is a valid point for both lines, which is 0, 1, or $\infty$ number of points. For reference, go to: http://www.mathsisfun.com/algebra/systems-linear-equations.html And scroll down to "Solutions"

loser66 · Answer

oh, I misunderstand the "linear" word. I am sorry, I over think the problem. hehehe. Let me take off my wrong comments.

anonymous · Answer

i learn something new each day :) sorry

ranga · Answer

We all do. :)

e.mccormick · Answer

When you get 3 linear equations in 3 unknowns you get a similar result, but it can be no solution, a point, a line, a plane, or a space.  Both a plane and a space are $\infty$ number of solutions, but a space is a larger $\infty$ than a plane.

loser66 · Answer

go to faaaar above my head. hehehe.. sorry

e.mccormick · Answer

Oh, and a line is also $\infty$ sol, and the smallest $\infty$ of the three....  Hehe.  So even $\infty$ has different sizes.