Answer
The system has no real solutions.
Work Step by Step
The given system is
$y=-3x^2+2x+1$ ...... (1)
$y=5-3x$ ...... (2)
Substitute $5-3x$ for $y$ in equation (1).
$\Rightarrow 5-3x=-3x^2+2x+1$
Add $3x-5$ to each side.
$\Rightarrow 5-3x+3x-5=-3x^2+2x+1+3x-5$
Simplify.
$\Rightarrow 0=-3x^2+5x-4$
Find the number of real solutions.
$= b^2-4ac$
Substitute $-3$ for $a,5$ for $b,$ and $-4$ for $c$.
$= (5)^2-4(-3)(-4)$
Simplify.
$= 25-48$
Subtract.
$= -23$
Discriminant is less than $0$,
The equation has no real solutions.
Hence, the system has no real solutions.
