The number of solutions of the system of equations α^2x+α y = - 1 α x…

The correct answer is Option (3) → -1

for infinite no. of solution to exist

a1/a2=b1/b2=c1/c2

$\frac{α^2}{α}=\frac{α}{α^2}=\frac{-1}{1}$

so $α=-α^2⇒α^2+α=0$

so $α=0,1$

for $α=0$ not exists

so $α=-1$