Question

Solve the system of equations graphed.
y = -2x + 5. y = x - 4.
Responses (0,5) open paren 0 comma 5 close paren (−1,3) open paren negative 1 comma 3 close paren (5,−4) open paren 5 comma negative 4 close paren (3,−1)

Answer 1

To solve the system of equations given by:

1. \( y = -2x + 5 \)
2. \( y = x - 4 \)

we can set the expressions for \( y \) equal to find the point of intersection:

\[
-2x + 5 = x - 4
\]

Now, we'll solve for \( x \):

1. Add \( 2x \) to both sides:

\[
5 = 3x - 4
\]

2. Add \( 4 \) to both sides:

\[
9 = 3x
\]

3. Divide by \( 3 \):

\[
x = 3
\]

Now we can substitute \( x = 3 \) back into either equation to find \( y \). We'll use the second equation:

\[
y = x - 4 = 3 - 4 = -1
\]

So the solution to the system of equations is:

\[
(3, -1)
\]

Thus, the correct answer is

\[
\boxed{(3, -1)}
\]