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MaCey
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Tyro
Asked: 2021-04-13T14:09:02+00:00 In: ,

Solve the following

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Solve 4/x + 3y = 8 and 6/x -4y = -5

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  2. acedstud
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    Given \dfrac{4}{x}+3y=8, multiplying through by x gives 4+3xy=8x\Rightarrow8x-3xy=4\Rightarrow x(8-3y)=4\Rightarrow x=\dfrac{4}{8-3y}.

    Substituting x=\dfrac{4}{8-3y} into the second equation, \dfrac{6}{x}-4y=-5, we have \dfrac{6}{\frac{4}{8-3y}}-4y=-5\Rightarrow\dfrac{6(8-3y)}{4}-4y=-5\Rightarrow\dfrac{48-18y}{4}-4y=-5

    \Rightarrow12-4.5y-4y=-5\Rightarrow4.5y+4y=12+5\Rightarrow8.5y=17\Rightarrow\dfrac{8.5y}{8.5}=\dfrac{17}{8.5}

    \Rightarrow y=2.

    Substituting y=2 into x=\dfrac{4}{8-3y}, we have x=\dfrac{4}{8-3(2)}=\dfrac{4}{8-6}=\dfrac{4}{2}=2

    Therefore, x=2 and y=2.

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