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Math Help - Solving 2 equations with 1 variable

  1. #1
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    Solving 2 equations with 1 variable

    I'm having trouble with this. i know it's simple, but I'm honestly blanking out on how to do this:

    2 equations:

    X = 12L - 0.75L^2
    A = 24L - 2.25L^2

    What does L equal when X and A intersect?

    I know this means when X = A, which is 12L - 0.75L^2 = 24L - 2.25L^2

    The answer is X = A at 8 but how do I find this?
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  2. #2
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    Re: Solving 2 equations with 1 variable

    12l - 0.75l^2 = 24l - 2.25l^2

    1.5l^2 - 12l = 0

    1.5l(l - 8) = 0

    l = 0 , l = 8
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    Re: Solving 2 equations with 1 variable

    I understand what you did up to the third line, could you explain that?

    did you do 12/1.5 to get 8?
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    Re: Solving 2 equations with 1 variable

    Oh okay, I get it!! You factored the second part. but where do you find L = 100?
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    Re: Solving 2 equations with 1 variable

    Quote Originally Posted by snypeshow View Post
    Oh okay, I get it!! You factored the second part. but where do you find L = 100?
    L = 0 , not 100
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    Re: Solving 2 equations with 1 variable

    Sorry about that (I was trying to apply what you did two another exercise), I meant: Where do you find L = 8?
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    Re: Solving 2 equations with 1 variable

    Do you know how to solve quadratic equations? As skeeter showed, with A= X, you have 12L- .75L^2= 24L- 2.25L^2. Adding 2.25L^2 to both sides and subtracting 24L from both sides, you get 1.5L^2- 12L= 0. The simplest way to solve a quadratic equation is to factor (if you can). Here, we can see there is an "L" in both parts so we can factor that out: L(1.5L- 12)= 0. The crucial arithmetic point here is that if ab= 0, then either a= 0, or b= 0, or both. If the first factor, L, is 0, then, of course, we get the solution L= 0. If the other factor, 1.5L- 12= 0, we have 1.5L= 12 and then L= 12/1.5. 1.5 is, of course, the same as 3/2 and dividing by 3/2 is the same as multiplying by 2/3: = 12(2/3)= 24/3= 8.
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    Re: Solving 2 equations with 1 variable

    I know how to solve quadratic equations, but yeah, I never thought of solving it through factoring!! Thanks for the explanation HallsofIvy!!
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