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I would expect integer solutions. If you change the problem to
then your algebraic procedure will produce integer solutions. With the problem as originally worded I don't se a solution except to use algebra as you did. With my change you have two numbers that satisfy
From here you might be able to find the numbers using "Guess and Check". Look for factors of 120 and calculate their sum.
I hope this helps,
Hi Michelle, There are three methods for solving systems of equations: substitution, elimination & graphing. A less accurate way to find the solution would be graphing x+y=25 & xy=120 and find the point where they intersect. if you have a graphing program it usually has a tool that will find intersections for you. If the numbers were integers then guess and check would also be an option. Hope this helps,  


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