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How can I find Y from two equations WITHOUT using X?

  1. Sep 23, 2007 #1
    How can I find Y from two equations WITHOUT using X:

    (1) Xcos(Z) - Ycos(W) = 0

    (2) Xsin(Z) + Ysin(W) - mg = 0

    Now I have found out that

    Y = Xcos(Z) / cos(W) and also

    Y = mg - Xsin(Z) / sin(W)

    How can I eliminate X from these two equations ??

    Me algebra isn't good....
     
  2. jcsd
  3. Sep 23, 2007 #2

    AlephZero

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    I hope you meant

    Y = (mg - Xsin(Z)) / sin(W)

    the extra brackets are important!

    It's easy to eliminate Y from the two equations you got.

    Xcos(Z) / cos(W) = (mg - Xsin(Z)) / sin(W)

    But you wanted to eliminate X, not Y. So start again and rearrange the two equations as

    X = .......

    not as Y = .......
     
  4. Sep 23, 2007 #3

    arildno

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    Rewrite your first equation as:
    Xcos(z)=Ycos(w)

    Does any bell ring for you?
    Some manipulation you may make to solve for X, in terms of Y, w and z?
     
  5. Sep 23, 2007 #4
    Well, I'm trying to eliminate X frome (1) and (2) so I can solve Y in terms of anything BUT X.

    I'm sorry but Xcos(z)=Ycos(w) doesn't ring any bell for me
     
  6. Sep 23, 2007 #5

    arildno

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    Well, as long as Cos(z) does not equal 0, we have:
    [tex]X=Y\frac{\cos(w)}{\cos(z)}[/tex]

    Thus, inserting this on the X's place in your second equation, you get:
    [tex]Y\cos(w)\tan(z)+Y\sin(w)=mg[/tex]
    whereby you get:
    [tex]Y=\frac{mg}{\cos(w)\tan(z)+\sin(w)}[/tex]
     
  7. Sep 23, 2007 #6
    Ok! That was the simple rule I was looking for! Ycos(w)/cos(z) = Ycos(w)tan(z)

    Thank you very much!
     
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