Question 141118: How do you know when an equation has an infinitely number of solutions or when an equation has no solution?
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! An equation has infinitely many solutions when, in the process of solving for the variable, you come down to a statement (for example, 0=0) that is ALWAYS TRUE. In math, this is called an IDENTITY.
An equation has NO SOLUTIONS when, in the process of solving for the variable, all of the variables subtract out, and you get a statement (for example, 0=3)that is NEVER TRUE. This is called a CONTRADICTION.
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