June 3rd, 2018, 08:07 PM  #1 
Member Joined: Apr 2017 From: India Posts: 45 Thanks: 0  System of equations
There is no system of linear equations over R that has exactly two solutions. True or False. Justify your answer with a short proof or by a counter example.

June 3rd, 2018, 08:09 PM  #2 
Senior Member Joined: Aug 2012 Posts: 2,157 Thanks: 631 
If there were two solutions, what would that mean geometrically?

June 3rd, 2018, 09:59 PM  #3 
Member Joined: Apr 2017 From: India Posts: 45 Thanks: 0  confused. Well to be clear to you, What I know is, either there are infinitely many solutions or unique solution or no solution for a system of linear equations. But for exactly two solutions, I am confused. As per me the above statement should be true and there is no system of linear equations with exactly two solutions. Do you agree with my reasoning or not? Also, if there are exactly two solutions, then the equation must be quadratic. (Something different in my mind, right now). Last edited by shashank dwivedi; June 3rd, 2018 at 10:05 PM. Reason: incomplete response 

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