Answer
$(0, -1)$ and $(1, 0)$
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:
$3x^2 - 2x - 1 = x - 1$
We want to move all terms to the left side of the equation.
$3x^2 - 2x - x - 1 + 1 = 0$
Combine like terms:
$3x^2 - 3x = 0$
Factor out any common terms:
$3x(x - 1) = 0$
Set each factor equal to $0$.
First factor:
$3x = 0$
Divide each side of the equation by $3$:
$x = 0$
Second factor:
$x - 1 = 0$
Add $1$ to each side of the equation:
$x = 1$
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:
$y = x - 1$
Substitute the solution $0$ for $x$:
$y = 0 - 1$
Add to solve:
$y = -1$
Let's solve for $y$ using the other solution, $x = 1$:
$y = 1 - 1$
Subtract to solve:
$y = 0$
The solutions are $(0, -1)$ and $(1, 0)$.
