Q80 / 120 · VITEEE 2011 · Mathematics

The system of equations $2 x+y-5=0$, $x-2 y+1=9,2 x-14 y-a=0$, is consistent. Then, $a$ is equal to

  • A
    1
  • B
    2
  • C
    5
  • Correct answer
    D
    None of these

Solution

Given system of equations are $$ \begin{array}{l} 2 x+y-5=0 ...(i)\\ x-2 y+1=0...(ii) \end{array} $$ and $2 x-14 y-a=0...(ii)$ This system is consistent $$ \begin{array}{l} \therefore\left|\begin{array}{ccc} 2 & 1 & -5 \\ 1 & -2 & 1 \\ 2 & -14 & -\mathrm{a} \end{array}\right|=0 \\ \Rightarrow 2(2 \mathrm{a}+14)-1(-\mathrm{a}-2)-5(-14+4)=0 \\ \Rightarrow 4 \mathrm{a}+28+\mathrm{a}+2+50=0 \\ \Rightarrow 5 \mathrm{a}=-80 \Rightarrow \mathrm{a}=-16 \end{array} $$

Hence, the correct answer is option: 'D'.

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