Answer
The system has no real solutions.
Work Step by Step
The given system is
$y=x^2+x+1$ ...... (1)
$y=-x-2$ ...... (2)
Subtract equation (2) from equation (1).
$\Rightarrow y-y=x^2+x+1-(-x-2)$
$\Rightarrow y-y=x^2+x+1+x+2$
Simplify.
$\Rightarrow 0=x^2+2x+3$
Find the number of real solutions.
$= b^2-4ac$
Substitute $1$ for $a,2$ for $b,$ and $3$ for $c$.
$= (2)^2-4(1)(3)$
Simplify.
$= 4-12$
Subtract.
$= -8$
Discriminant is less than $0$,
The equation has no real solutions.
Hence, the system has no real solutions.
