Question

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

• A. $1$
• B. $2$
• C. $5$
• D. None of these

Answer 1

Answer: (D)

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