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Math Help - Variables within variables? Simultaneous equation solutions

  1. #1
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    Variables within variables? Simultaneous equation solutions

    I have been asked to find real values for m such that this system of equations has no solution, infinitely many solutions and exactly one solution:

    2x-2y=5

    10x-10y=m

    At first I thought that the question wanted me to find a value for each scenario, but I could only find a value that gave infinitely many solutions: m = 25. I can see that they are essentially the same line so any value other than 25 would just shift it up or down and cause the two lines to never intersect.

    I couldn't see any other real value for m could produce any solutions until I though what if m = 10y ?

    10x-10y=10y

    y = 0 (sub into first equation)

    Am I way off track with this question?

    2x = 5

    x = \frac{5}{2}

    Does that count? I guess there would be infinitely many ways to do that though...
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  2. #2
    Super Member Quacky's Avatar
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    Re: Variables within variables? Simultaneous equation solutions

    No, you're not off track. The only way there are infinite solutions for real values of m are when m=25, and the only way there are no solutions are when m\neq{25}

    I can't see any way to find real values of m that give 'just one solution'.
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