Question

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

Answer 1

Answer: (D)

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