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. $Infinitelymany$

Answer 1

The correct option is C $2$

For more than one solutions,

$⟹\frac{a}{1}=\frac{1}{(a+10)}$

$⟹a^2+10a=1$

$⟹a^2+10a-1=0$

Now,

$\because$ $Discriminant$ $=B^2-4AC$

$={100}^2-4\times 1\times (-1)$

$⟹D=104$

is Greater than zero

$\therefore$ It has 2 different solution .