Answer
No solution
Work Step by Step
$y=2x^2+1$
$x+y=-1$
$x+y=-1$
$x+y-x=-1-x$
$y=-x-1$
$y=2x^2+1$
$y=-x-1$
$2x^2+1=-x-1$
$2x^2+1+x+1=-x-1+x+1$
$2x^2+x+2=0$
$a=2$, $b=1$, $c=2$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-1±\sqrt {1^2-4*2*2})/2*1$
$x=(-1±\sqrt {1-16})/2$
$ x=(-1±\sqrt {-15})/2$
Since we have the square root of a negative number, we find that there is no solution for this system of equations.