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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2012

  • question_answer
    The system of equations\[2x+y-5=0,\] \[x-2y+1=0\]and\[2x-14y-a=0\]is consistent. Then, a is equal to

    A)  1            

    B)  2

    C)  5            

    D)  None of these

    Correct Answer: D

    Solution :

    The given system of equation is \[2x+y-5=0\] \[x-2y+1=0\] and        \[2x-14y-a=0\] This system is consistent. \[\therefore \] \[\left| \begin{matrix}    2 & 1 & -5  \\    1 & -2 & 1  \\    2 & -14 & -a  \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[2(2a+14)-1(-a-2)-5(-14+4)=0\] \[\Rightarrow \] \[4a+28+a+2+50=0\] \[\Rightarrow \]            \[5a=-80\] \[\Rightarrow \]   \[a=-16\]


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