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Math Help - Method of Substitution! Help!

  1. #1
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    Method of Substitution! Help!

    Use the method of substitution to solve the system



    Answer for should be in (_,_),(_,_) form or just (_,_) form.

    Thanks!
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  2. #2
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    Since x + y = 1, you can deduce that {\color{blue}y = 1 - x}.

    Plug this to the original equation:
    x^{2} + {\color{blue} y^{2}} = 8
    x^{2} + {\color{blue} (1-x)^{2}} = 8

    Continue on and solve for x then y.
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by luigiandme View Post
    Use the method of substitution to solve the system



    Answer for should be in (_,_),(_,_) form or just (_,_) form.

    Thanks!
    lets isloate one variable in the bottom equation lets say y.

    x+y=1 \iff y=1-x

    Now will will sub this into the first equation for y.

    x^2+(1-x)^2=8 expand the left hand side

    x^2+1-2x+x^2=8 \iff 2x^2-2x=7

    2(x^2+x+\frac{1}{4})=7+2\cdot \frac{1}{4}

    2(x+\frac{1}{2})^2=\frac{15}{2} \iff (x+\frac{1}{2})^2=\frac{15}{4}

    x=-\frac{1}{2} \pm \frac{\sqrt{15}}{2}

    plug this back in to find the values for y
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  4. #4
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    hmm.. im sorry but i just cant seem to be getting the correct answer after plugging it in! This is driving me nuts...
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  5. #5
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    Quote Originally Posted by TheEmptySet View Post
    lets isloate one variable in the bottom equation lets say y.

    x+y=1 \iff y=1-x

    Now will will sub this into the first equation for y.

    x^2+(1-x)^2=8 expand the left hand side

    x^2+1-2x+x^2=8 \iff 2x^2-2x=7

    2(x^2 {\color{red}-}x+\frac{1}{4})=7+2\cdot \frac{1}{4}

    2(x{\color{red}-}\frac{1}{2})^2=\frac{15}{2} \iff (x{\color{red} -}\frac{1}{2})^2=\frac{15}{4}

    x={\color{red}+}\frac{1}{2} \pm \frac{\sqrt{15}}{2}

    plug this back in to find the values for y
    A little mistake ...
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