Answer
$(0, -1)$.
Work Step by Step
We will use substitution to solve this system of equations. We substitute one of the expressions for $y$, which would mean that we are going to set the two equations equal to one another to solve for $x$ first:
$x^2 - 2x - 1 = -x^2 - 2x - 1$
We want to move all terms to the left side of the equation.
$x^2 + x^2 - 2x + 2x - 1 + 1 = 0$
Combine like terms:
$2x^2 = 0$
Divide each side by $2$:
$x^2 = 0$
Take the square root of both sides of the equation:
$x = 0$
Now that we have the possible value for $x$, we can plug it into one of the original equations to find the corresponding $y$ value. Let's use the first equation:
$y = x^2 - 2x - 1$
Substitute the solution $0$ for $x$:
$y = 0^2 - 2(0) - 1$
Evaluate exponent first:
$y = 0 - 2(0) - 1$
Multiply to simplify:
$y = 0 - 0 - 1$
Add from left to right:
$y = -1$
The solution is $(0, -1)$.
