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Math Help - Systems of nonlinear equations in two variables- Need help with 2 problems

  1. #1
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    Exclamation Systems of nonlinear equations in two variables- Need help with 2 problems

    Can you please me with the following problems:

    Solve by the method of your choice.

    x^2+y^2=50
    (x-7)^2+y^2=1

    I tried to find a variable that I could isolate and I wasnt sure what to mulitply by in order to get a variable to isolate.

    x^2+y^2=29
    -8x+y^2=41

    this is as far as I got:

    8(x^2+y^2=29)

    now I got:

    8x^2+y^2=232
    -8x+y^2=41

    but I still cant isolate anything.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by soly_sol View Post
    Can you please me with the following problems:

    Solve by the method of your choice.

    x^2+y^2=50
    (x-7)^2+y^2=1
    Typically in Physics we tend to use the "substitution method." But in this particular case the substitution method is going to rather messy. What I would do is subtract the second equation from the first:
    (x^2+y^2) - (x-7)^2+y^2) = 50 - 1

    x^2 - (x - 7)^2 = 49
    and go from there.

    -Dan
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by soly_sol View Post
    x^2+y^2=29
    -8x+y^2=41
    Watch your multiplication: You have to multiply everything on both sides of the equation by 8, not just one term.

    Here you could use substitution. Solve the second equation for x:
    x = \frac{1}{8}(y^2 - 41)

    Then insert this value of x into the first equation:
    \left ( \frac{1}{8}(y^2 - 41) \right ) ^2+y^2=29

    It'll take a while, but its doable.

    The other way is faster: just subtract both equations again:
    (x^2+y^2) - ( -8x+y^2) = 29 - 41

    x^2 + 8x = -12
    etc.

    -Dan
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