Answer
The solution is $(0, -5)$.
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:
$-x^2 + x - 5 = x - 5$
We want to move all terms to the left side of the equation.
$-x^2 + x - x - 5 + 5 = 0$
Combine like terms:
$-x^2 = 0$
Divide both sides by $-1$:
$x^2 = 0$
Take the square root of both sides of the equation:
$x = 0$
Now that we have the value for $x$, we can plug it into one of the original equations to find the corresponding $y$ value. Let's use the second equation:
$y = x - 5$
Substitute the solution $0$ for $x$:
$y = 0 - 5$
Add to solve:
$y = -5$
The solution is $(0, -5)$.
