Answer
The system has no real solutions.
Work Step by Step
The given system is
$y=2x+5$ ...... (1)
$y=-3x^2+x-4$ ...... (2)
Subtract equation (2) from equation (1).
$\Rightarrow y-y=2x+5-(-3x^2+x-4)$
$\Rightarrow y-y=2x+5+3x^2-x+4$
Simplify.
$\Rightarrow 0=3x^2+x+9$
Find the number of real solutions.
$= b^2-4ac$
Substitute $3$ for $a,1$ for $b,$ and $9$ for $c$.
$= (1)^2-4(3)(9)$
Simplify.
$= 1-108$
Subtract.
$= -107$
Discriminant is less than $0$,
The equation has no real solutions.
Hence, the system has no real solutions.
