Question

Let $a,b,c,d,u,v$ be integers. If the system of equations $ax+by=u,cx+dy=v$ has a unique solution, then

• A. $ad-bc=0$
• B. $ad-bc=-1$
• C. $ad-bc\ne 0$
• D. $ad-bc>0$

Answer 1

Answer: (C)

$ad-bc\ne 0$

Given system of equations $ax+by=u,cx+dy=v$ has a unique solution.

$\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}u\\ v\end{array}\right]$

$\Rightarrow \Delta =\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|\ne 0$

$\therefore ad-bc\ne 0$

Hence, option $C$.