Question

If the system of linear equations
$\begin{array}{c}x-4y+7z=7g\\ 3y-5z=h\\ -2x+5y-9z=k\end{array}$

is consistent, then :

• A. $2g+h+k=0$
• B. $g+2h+k=0$
• C. $g+h+2k=0$
• D. $g+h+k=0$

Answer 1

The correct option is A $2g+h+k=0$

$\Delta =\left|\begin{array}{ccc}1& -4& 7\\ 0& 3& -5\\ -2& 5& -9\end{array}\right|=0$

Since, system of linear equations is consistent,
$\therefore \Delta ={\Delta }_1={\Delta }_2={\Delta }_3=0$
${\Delta }_3=0$
$\Rightarrow 2g+h+k=0$