Question

Find the solution(s) to the system of equations.
Select all that apply.
Math
Description
y=x2-1
y =2x-2
0 (0, 1)
O (-2,0)
0 (-1,0)
0 (1,01

Answer 1

To find the solutions to the system of equations given by \(y = x^2 - 1\) and \(y = 2x - 2\), we can set the equations equal to each other:

\[
x^2 - 1 = 2x - 2
\]

Rearranging this equation, we can move all terms to one side:

\[
x^2 - 2x + 1 = 0
\]

This simplifies to:

\[
(x - 1)^2 = 0
\]

Thus, we find:

\[
x - 1 = 0 \quad \Rightarrow \quad x = 1
\]

Now, to find the corresponding \(y\) value, we can substitute \(x = 1\) back into either of the original equations. We'll use the linear equation \(y = 2x - 2\):

\[
y = 2(1) - 2 = 0
\]

So, the point of intersection is \((1, 0)\).

Now we have one solution, which is \((1, 0)\).

Next, let's check the given options:

- \( (0, 1) \)
- \( (-2, 0) \)
- \( (-1, 0) \)
- \( (1, 0) \)

Based on our findings, the only valid solution from the options provided is:

- \( (1, 0) \)

Thus, the answer is \( (1, 0) \).