Question

Use graphing technology to find the solutions to the linear-quadratic system of equations:

y=x2−3x−4
y
=
x
2
−
3
x
−
4

y=−x−1
y
=
−
x
−
1

Which answer gives the solutions to the system of equations?

(1 point)
Responses

(−1,0)
(
−
1
,
0
)
and (4,0)
(
4
,
0
)
open paren negative 1 comma 0 close paren and open paren 4 comma 0 close paren

(−1,0)
(
−
1
,
0
)
and (3,−4)
(
3
,
−
4
)
open paren negative 1 comma 0 close paren and open paren 3 comma negative 4 close paren

(0,−1)
(
0
,
−
1
)
and (−4,3)
(
−
4
,
3
)
open paren 0 comma negative 1 close paren and open paren negative 4 comma 3 close paren

(0,−1)
(
0
,
−
1
)
and (0,−4)

Answer 1

To solve the system of equations given by \( y = x^2 - 3x - 4 \) and \( y = -x - 1 \), we can set the equations equal to each other:

\[
x^2 - 3x - 4 = -x - 1
\]

Rearranging this gives:

\[
x^2 - 3x + x - 4 + 1 = 0
\]
\[
x^2 - 2x - 3 = 0
\]

Next, we can factor the quadratic equation:

\[
(x - 3)(x + 1) = 0
\]

This gives us the solutions for \( x \):

\[
x - 3 = 0 \quad \Rightarrow \quad x = 3
\]
\[
x + 1 = 0 \quad \Rightarrow \quad x = -1
\]

Now we will find the corresponding \( y \) values for each \( x \).

1. For \( x = 3 \):
\[
y = -3 - 1 = -4 \quad \Rightarrow \quad (3, -4)
\]

2. For \( x = -1 \):
\[
y = -(-1) - 1 = 0 \quad \Rightarrow \quad (-1, 0)
\]

Thus, the solutions to the system of equations are \( (-1, 0) \) and \( (3, -4) \).

Checking the provided responses, the correct answer is:

**(−1, 0) and (3, −4)**.