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Question 214801: How do you know when an equation has infinately many solutions?
Answer by drj(1380)   (Show Source):
You can put this solution on YOUR website! How do you know when an equation has infinitely many solutions?
Step 1. Let's say you have two equations:
x+y=5 Equation A
2x+2y=10 Equation B
Step 2. We can see that Equation A is the same as Equation B if we divide equation B by 2 or we can subtract B from A and get Equation A. When we get the same equation based on another equation, these equations are said to be dependent. And so there will be many solutions to the equations since we really have only one equation for two variables x and y. In our example, Equations A and B are dependent. In the above example there are many variables x and y or solutions (x,y) that will satisfy Equations A and B. As mentioned before, the two equations. are the same line have infinite number of points in common.
Step 3. SHORT ANSWER: So if we have more variables than equations then we have an infinite number of solutions.
I hope the above explanation was helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
Good luck in your studies!
Respectfully,
Dr J
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