Question

If the system of equations $x-2y=1,x+ky+4=0$ and $2x+y=3$ is consistent, then the value of $k$ is:

• A. $3$
• B. $9$
• C. $27$
• D. $-27$

Answer 1

The correct option is D $-27$

For the system of equations $x-2y=1,x+ky+4=0$ and $2x+y=3$ to be consistent, $\left|\begin{array}{ccc}1& -2& 1\\ 1& k& -4\\ 2& 1& 3\end{array}\right|=0$
$\Rightarrow (3k+4)+2\left(11\right)+(1-2k)=0$
$\Rightarrow k=-27$