Question 120712: how do you know when an equation has an infinite amount of solutions or no solution?
Answer by nabla(475)   (Show Source):
You can put this solution on YOUR website! The answer to this question will sometimes vary depending on which area of mathematics you are considering. However, in general:
if you get a result such as 0=0, this implies a true statement, and as such is the case, any value of a particular variable will work.
Example: Consider this system of equations:
If we solve the first equation for y, we get  ,
now substituting this y into the second equation,
as you can see, we will get the statement  . Thus, gives us a y value for any x that we can choose. Moreover, y is the dependent variable.
On the other hand, you can sometimes get a result such as  , which is a false statement. This implies that there is no solution to an equation or a system of equations.
Example: Consider this system of equations:
Solve for y in the first equation: 
substitute this into the second equation:  . As you can see, this will result in the statement that  which is false, there are no values of x or y that make that system true.
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