Question

The system of equations $2\,x + y -5=0, x - 2\,y + 1 = 9, 2\,x -14y\, - a = 0$, 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
$2\,x + y - 5 = 0\,...(i)$
$x - 2\,y + 1 = 0\,...(ii)$
and $2\,x - 14\,y - a = 0\,...(iii)$
This system is consistent
$\therefore \begin{vmatrix}2&1&-5\\ 1&-2&1\\ 2&-4&-a\end{vmatrix}=0$
$\Rightarrow 2 \left(2a + 14\right) - 1 \left(-a -2\right) - 5 \left(-14 + 4\right) = 0$
$\Rightarrow 4\,a + 28 + a + 2 + 50 = 0$
$\Rightarrow 5\,a = -80 $
$\Rightarrow a = -16$