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Math Help - Eliminating x and y

  1. #1
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    Post Eliminating x and y

    Hi there I have a problem that I am trying to figure out. It said that by eliminating x and y from the equations \frac {1}{y}+\frac {1}{y}=1, x +y = a, \frac {y}{x}=m where a =/0. obtain a relation between m adn a. Given that a is real, determine the ranges of values of a for which m is real. Can some one help me with this problem. Thank you in advance.
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  2. #2
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    I'm guessing the first term should be 1/x rather than another 1/y?

    Solve the second for x and substitute this expression into the other two equations. You'll be nearly done.
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    I'm guessing the first term should be 1/x rather than another 1/y?

    Solve the second for x and substitute this expression into the other two equations. You'll be nearly done.
    I tried that and I am just not getting the problem solved at all.for the second I got x=a-y but when I substitute that value for the other two eqaution every thing just seem confusing from there.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by scrible View Post
    I tried that and I am just not getting the problem solved at all.for the second I got x=a-y but when I substitute that value for the other two eqaution every thing just seem confusing from there.
    Perhaps this is a bit sloppy (but then I tend to make problems a bit rougher than they need to be.) Start with the two equaitons:
    \frac{1}{x} + \frac{1}{y} = 1
    and
    x + y = a

    Then we know that
    \frac{x + y}{xy} = 1

    Put the second equation in:
    \frac{a}{x(a - x)} = 1

    or
    x^2 - ax + a = 0

    Now start from x + y = a and y = mx.
    x + mx = a

    giving
    x = \frac{a}{m + 1}

    Put this into the x^2 - ax + a = 0 equation to cancel the x and you are done.

    -Dan
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  5. #5
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    Quote Originally Posted by topsquark View Post
    Perhaps this is a bit sloppy (but then I tend to make problems a bit rougher than they need to be.) Start with the two equaitons:
    \frac{1}{x} + \frac{1}{y} = 1
    and
    x + y = a

    Then we know that
    \frac{x + y}{xy} = 1

    Put the second equation in:
    \frac{a}{x(a - x)} = 1

    or
    x^2 - ax + a = 0

    Now start from x + y = a and y = mx.
    x + mx = a

    giving
    x = \frac{a}{m + 1}

    Put this into the x^2 - ax + a = 0 equation to cancel the x and you are done.

    -Dan
    Thank you very much
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