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Math Help - needdd major help solving a system

  1. #1
    Newbie
    Joined
    Dec 2006
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    needdd major help solving a system

    how wouls u solve this

    y=x+4
    x^2+y^2=16

    the questions says:

    solving a liner-quadratic system involves finding the values which satasfy a liner equation and a quadratic equation simultaneously. The method of substituting the inear equation into the quadratic equation should be used. The quadratic equation could b a parabola or a circle or any of the conic sections. The values found in the solution represent the co-ordiantes of the point(s) of intersection of the two graphs.

    solve the set of real numbers.

    can you show me how to do this and explain the steps please
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, kishan!

    \begin{array}{cc}y\:=\:x+4 \\ x^2+y^2\:=\:16\end{array}

    "The method of substituting the inear equation into the quadratic equation should be used."
    What part of that don't you understand?

    Substitute y\:=\:x+4 into x^2 + y^2\:=\:16

    We have: . x^2 + (x + 4)^2\:=\:16

    Then: . x^2 + x^2 + 8x + 16 \:=\:16\quad\Rightarrow\quad 2x^2 + 8x\:=\:0

    Factor: . 2x(x+4)\:=\:0

    And we have two roots: . \begin{array}{cc}2x\:=\:0 \\ x + 4\:=\:0 \end{array}<br />
\begin{array}{cc}\Rightarrow \\ \Rightarrow \end{array}<br />
\begin{array}{cc}x\,=\,0 \\ x\,=\,\text{-}4\end{array}

    The corrsponding y-values are: . y \:=\:4,\,0


    Answers: . \begin{Bmatrix}x=0, & y=4 \\ x=\text{-}4, & y=0\end{Bmatrix}

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