Answer
The solutions are $(0,2)$ and $(-6,-22)$.
Work Step by Step
The given system is
$y=-x^2-2x+2$ ...... (1)
$y=4x+2$ ...... (2)
Subtract equation (2) from equation (1).
$\Rightarrow y-y=-x^2-2x+2-(4x+2)$
$\Rightarrow y-y=-x^2-2x+2-4x-2$
Simplify.
$\Rightarrow 0=-x^2-6x$
Factor out $-x$ from each side.
$\Rightarrow 0=-x(x+6)$
Use zero product property.
$\Rightarrow -x=0$ or $x+6=0$
Solve for $x$.
$\Rightarrow x=0$ or $x=-6$
Substitute $0$ for $x$ in equation (2).
$\Rightarrow y=4(0)+2$
Simplify.
$\Rightarrow y=2$
Substitute $-6$ for $x$ in equation (2).
$\Rightarrow y=4(-6)+2$
Simplify.
$\Rightarrow y=-24+2$
$\Rightarrow y=-22$
Hence, the solutions are $(0,2)$ and $(-6,-22)$.
