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I was trying to find the values of two unknown variables using two equations.When I simplified both the equations, both of them were the same. What should be the value of the variables in such a case?

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Usually this means that there are multiple solutions. You can select the value of one variable arbitrarily and then solve for the other. But there are exceptions to this, depending on the precise shapes of your equations. Please show them! –  Henning Makholm Oct 8 '11 at 16:10
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Indeed, we can be more helpful if you show what you actually have... –  J. M. Oct 8 '11 at 16:12
    
@HenningMakholm: They were some algebraic equations.. –  Fahad Uddin Oct 22 '11 at 10:25
    
But secret, apparently. You cannot expect any useful help for people you refuse to show the problem to. If it's a matter of national security, doesn't your agency have an internal department for solving classified equations? –  Henning Makholm Oct 22 '11 at 12:49
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up vote 1 down vote accepted

In many cases, you can choose one variable as free parameter and then calculate the value of the other variable using that parameter which gives infinitely many solutions.

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This would give rise to multiple solutions.. –  Fahad Uddin Oct 14 '11 at 16:47
    
Yes, this is to be expected to happen often when you have actually just one equation for two variables. –  Phira Oct 14 '11 at 16:56
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