Answer
The system has no real solutions.
Work Step by Step
The given system is
$y=-2x^2+x-3$ ...... (1)
$y=2x-2$ ...... (2)
Subtract equation (2) from equation (1).
$\Rightarrow y-y=-2x^2+x-3-(2x-2)$
$\Rightarrow y-y=-2x^2+x-3-2x+2$
Simplify.
$\Rightarrow 0=-2x^2-x-1$
Find the number of real solutions.
$= b^2-4ac$
Substitute $-2$ for $a,-1$ for $b,$ and $-1$ for $c$.
$= (-1)^2-4(-2)(-1)$
Simplify.
$= 1-8$
Subtract.
$= -7$
Discriminant is less than $0$,
The equation has no real solutions.
Hence, the system has no real solutions.
