Q. If the equations $2x + 3y + 1 = 0,\ 3x + y - 2 = 0$ and $ax + 2y - b = 0$ are consistent, then
A) $a - b = 2$
B) $a + b + 1 = 0$
C) $a + b = 3$
D) $a - b - 8 = 0$
Explanation
(a)
Since, the given equations are consistent.
$\therefore\ \left| \begin{matrix}
2 & 3 & 1 \\
3 & 1 & - 2 \\
a & 2 & - b
\end{matrix} \right| = 0$
$\Rightarrow 2( - b + 4) - 3( - 3b + 2a) + 1(6 - a) = 0$
$\Rightarrow \ - 2b + 8 + 9b - 6a + 6 - a = 0$
$\Rightarrow 7b - 7a = - 14$
$\Rightarrow a - b = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.