Answer
$(0, -4)$ and $(2, -2)$
Work Step by Step
First, we need to get the $y$ term by itself for both equations:
$y = x^2 - x - 4$
$y = x - 4$
We will use substitution to solve this system of equations. We substitute one of the expressions given for the $y$ term, which would mean that we are going to set the two equations equal to one another to solve for $x$ first:
$x^2 - x - 4 = x - 4$
We want to move all terms to the left side of the equation:
$x^2 - x - x - 4 + 4 = 0$
Combine like terms:
$x^2 - 2x = 0$
Factor out any terms that are common:
$x(x - 2) = 0$
Set each factor equal to $0$.
First factor:
$x = 0$
Second factor:
$x - 2 = 0$
Add $2$ to each side of the equation:
$x = 2$
Now that we have the two possible values for $x$, we can plug them into one of the original equations to find the corresponding $y$ values. Let's use the second equation:
$y = x - 4$
Substitute the solution $0$ for $x$:
$y = 0 - 4$
Combine like terms:
$y = -4$
Let's solve for $y$ using the other solution $x = 2$:
$y = 2 - 4$
Combine like terms:
$y = -2$
The solutions are $(0, -4)$ and $(2, -2)$.
