Answer
Solution set is empty.
Work Step by Step
$y= 2x^{2} + 1$ Equation $(1)$
$x+y = -1$ Equation $(2)$
From Equation $(2)$
$y = -1-x$ Equation $(3)$
From Equation $(1)$ and Equation $(3)$
$ 2x^{2} + 1 = -1-x$
$ 2x^{2} + 1 +1 + x = 0$
$ 2x^{2} + x + 2 = 0$
Using quadratic formula, $a=2, b = 1, c=2$
$x = \frac{-b±\sqrt (b^{2}-4ac)}{2a}$
$x = \frac{-1±\sqrt (1^{2}-4(2)(2))}{2(2)}$
$x = \frac{-1±\sqrt (1-16)}{4}$
$x = \frac{-1±\sqrt (-15)}{4}$
Since $\sqrt (-15)$ is not a real number, there is no real solution.
Solution set is empty.
