Q. If the system of equations $2x + 3y + 5 = 0,\ x + ky + 5 = 0,\ kx - 12y - 14 = 0$ be consistent, then value of $k$ is
A) $- 2,\frac{12}{5}$
B) $- 1,\frac{1}{5}$
C) $- 6,\frac{17}{5}$
D) $6,\ - \frac{12}{5}$
Explanation
(c)
The homogenous linear system of equations is consistent $ie$, possesses trivial solution, if$\ \Delta \equiv \left| \begin{matrix}
2 & 3 & 5 \\
1 & k & 5 \\
k & - 12 & - 14
\end{matrix} \right| \neq 0$
$\Rightarrow 2( - 14k + 60) - 3( - 14 - 5k) + 5( - 12 - k^{2}) \neq 0$
$\Rightarrow 5k^{2} + 13k - 102 \neq 0$
$\Rightarrow (5k - 17)(k + 6) \neq 0$
$\Rightarrow k \neq - 6,\frac{17}{5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.