Question 224423: I have to explain how you know when an equation has Infinitely many solutions?.As well as how you know when they do not have any.
I think it is because in order for an equation to have infinitely many solutions you must have many variables, and if they do not have multiple variables then they would only have one solutions. am I correct in that thinking or am I missing something?
Found 2 solutions by rapaljer, Alan3354:
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! If you solve an equation for ONE variable, usually what happens you can solve for that variable by getting all the variables on one side and the number terms on the other side.
However, sometimes in the process of getting all the variables on one side, it just so happens that ALL the VARIABLES subtract out. In this case, you can't solve for the variable. Now, if all the variables subtract out, you will have an equatiaon or a statement that is either TRUE or it is FALSE!
If the resulting equation is always TRUE, then it will be TRUE no matter what! The statement is IDENTICALLY the same on the left and right side, so we call it an IDENTITY.
If the resulting equation is FALSE, then it will ALWAYS be FALSE. In this equaiton, there will be NO SOLUTIONS, no matter what you substitute for the variable. We all this a CONTRADICTION!!
R^2
Dr. Robert J. Rapalje
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! I have to explain how you know when an equation has Infinitely many solutions?.As well as how you know when they do not have any.
I think it is because in order for an equation to have infinitely many solutions you must have many variables, and if they do not have multiple variables then they would only have one solutions. am I correct in that thinking or am I missing something?
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x+y = 1 has an infinite number of solutions. You can pick any value for x and find a y.
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