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Question 478709: How do you know when an equation has an infinite number of solutions?
How do you know when an equation has no solution?
Found 2 solutions by solver91311, mananth:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
I think rather than "equation" you mean "system of equations" because that is the only way your question makes any sense. But I'm going to use the inconvenience of making you repost the question to teach you the lesson of the essential nature of precise communications. Repost with your question posed in correct terminology, and someone will help you.
John
My calculator said it, I believe it, that settles it
Answer by mananth(16946)  (Show Source):
You can put this solution on YOUR website! You have one solution ,no solution,OR infinite number of solutions for a system of equations. Not for a single line.
When they intersect – one solution
If the graph of the equations intersects each other at a point, then ordered pair corresponding to the point of intersection will be the solution to that system. In this case, the system will have exactly one solution. The slope and the y intercept will be different
When they are parallel – no solution
If the graphs of the equations are parallel, then the system of equations will have no solution. Because parallel lines never intersect each other.The slope will be the same but the Y intercept will be different
When they coincide- infinite solutions
If the graph of the equations coincides, then all the points on the line will be the solution to that system. In this case, the system will have infinite number of solutions. The slope and y intercept will be the same of both lines.
m.ananth@hotmail.ca
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