Tìm x,y biết `xy – \frac{x}{5} + \frac{y}{2} + y -x . 12 = 44`

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1. Đáp án:

    

   Giải thích các bước giải:

    $xy-\dfrac{x}{5}+\dfrac{y}{2}+y-12x=44$

   $⇔\dfrac{10xy}{10}-\dfrac{2x}{10}+\dfrac{5y}{10}+\dfrac{10y}{10}-\dfrac{120x}{10}=\dfrac{440}{10}$

   $ $

   $⇔10xy-2x+5y+10y-120x=440$

   $⇔10xy-122x+15y=440$

   $⇔2x.(5y-61)+15y=440$

   $⇔2x.(5y-61)+15y-183=440-183$

   $⇔2x.(5y-61)+3.(5y-61)=257$

   $⇔(2x+3).(5y-61)=257=257.1=1.257=(-1).(-257)=(-257).(-1)$

   $TH1:(2x+3).(5y-61)=257.1$

   $⇔x=127;y=\dfrac{62}{5}$

   $TH2:(2x+3).(5y-61)=1.257$

   $⇔x=-1;y=\dfrac{318}{5}$

   $TH3:(2x+3).(5y-61)=(-1).(-257)$

   $⇔x=-2;y=\dfrac{-196}{5}$

   $TH4:(2x+3).(5y-61)=(-257).(-1)$

   $⇔x=-130;y=12$

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