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Math Help - Systems of Equations and Inequalties?

  1. #1
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    Systems of Equations and Inequalties?

    I think I got the first steps right.Systems of Equations and Inequalties?-systems-equations-inequalities.jpgClick image for larger version. 

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  2. #2
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    Re: Systems of Equations and Inequalties?

    I think in the first equation i could of solved for y by dividing by x.
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  3. #3
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    Re: Systems of Equations and Inequalties?

    Hello, Melcarthus!

    Your canceling is incorrect.


    35.\;\begin{Bmatrix}xy^2 &=& 10^{11} & [1] \\ \\[-3mm] \dfrac{x^3}{y} &=& 10^{12} & [2]\end{Bmatrix}

    Divide [2] by [1]: . \dfrac{\frac{x^3}{y}}{xy^2} \:=\:\frac{10^{12}}{10^{11}} \quad\Rightarrow\quad \frac{x^3}{xy^3} \:=\:10 \quad\Rightarrow\quad x^2 \:=\:10y^3 \;\;[3]

    Square [1]: . (xy^2)^2 \:=\:(10^{11})^2 \quad\Rightarrow\quad x^2y^4 \:=\:10^{22}\;\;[4]

    Substitute [3] into [4]: . (10y^3)(y^4) \:=\:10^{22} \quad\Rightarrow\quad y^7 \:=\:10^{21} \quad\Rightarrow\quad \boxed{y \:=\:10^3}

    Substitute into [1]: . x(10^3)^2 \:=\:10^{11} \quad\Rightarrow\quad x(10^6) \:=\:10^{11} \quad\Rightarrow\quad \boxed{x \:=\:10^5}
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