Answer
The system has no real solutions.
Work Step by Step
The given system is
$y=-x+7$ ...... (1)
$y=-x^2-2x-1$ ...... (2)
Substitute $-x+7$ for $y$ in equation (2).
$\Rightarrow -x+7=-x^2-2x-1$
Add $x-7$ to each side.
$\Rightarrow -x+7+x-7=-x^2-2x-1+x-7$
Simplify.
$\Rightarrow 0=-x^2-x-8$
Find the number of real solutions.
$= b^2-4ac$
Substitute $-1$ for $a,-1$ for $b,$ and $-8$ for $c$.
$= (-1)^2-4(-1)(-8)$
Simplify.
$= 1-32$
Subtract.
$= -31$
Discriminant is less than $0$,
The equation has no real solutions.
Hence, the system has no real solutions.
