Question

For how many different values of $a$ does the following system have at least two distinct solutions?
$ax+y=0$
$x+(a+10)y=0$

• A. $0$
• B. $1$
• C. $2$
• D. Infinitely many

Answer 1

The correct option is C $2$

$y=-ax(a+10)y=-x$
$\frac{1}{a+10}=\frac{-a}{-1}$
$\Rightarrow a^2+10a-1=0$
As $D=100-4(-1)>0,$ so there exist two real and distinct values of $a$ for which the given system have at least two distinct solution.