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VIT Engineering VIT Engineering Solved Paper-2011

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

    A)  1

    B)  2

    C)  5

    D)  None of these

    Correct Answer: D

    Solution :

    Given, system of equations are \[2x+y-5=0\] ?(i) \[x-2y+1=0\] ?(ii) and \[2x-14y-a=0\] ?(iii) Since, 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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