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

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

Rajasthan PETRajasthan PET 2012

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 $