Question

For what value of $\alpha$, the system of equations $\alpha x+3=\alpha -3$ and $12x+\alpha y=\alpha$ will have a unique solution?

• A. $\alpha \ne \pm 6$
• B. $\alpha \ne \pm 3$
• C. $\alpha \ne \pm 5$
• D. None of these

Answer 1

The correct option is A $\alpha \ne \pm 6$

Since, the given equations have unique solution.

$\therefore \frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

$\frac{\alpha }{12}\ne \frac{3}{\alpha }$

$\Rightarrow {\alpha }^2\ne 36\Rightarrow \alpha \ne \pm 6$.