SOLUTION: How do you know when an equation has infinitely many solutions? How do you know when an equation has no solution?

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Question 143404: How do you know when an equation has infinitely
many solutions?
How do you know when an equation has no solution?

Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
Consider x+y=5. This implies y=5-x. What values of x can you plug in on the right side to get an answer? Infinitely many!
Now, consider 0=2. Is this correct? No. This means there is no solution--- there is nothing you can do algebraically to make the relationship true without altering it.
In general, infinitely many solutions means you can substitute any value for some variable(s) and get infinitely many answers. No solution applies when you can not find any solution to make a relationship true.
I can explain further, particularly through the use of systems of equations. E-mail me at enabla@gmail.com if you're interested.