Question

Solve the system of equations.

y=−3x+3


y=2x−7


(1 point)
Responses

(2,−3)
open paren 2 comma negative 3 close paren

(0,2)
open paren 0 comma 2 close paren

(−6,−2)
open paren negative 6 comma negative 2 close paren

no solution

Answer 1

To solve the system of equations given by:

1. \( y = -3x + 3 \)
2. \( y = 2x - 7 \)

we can set the two equations equal to each other since they both equal \( y \):

\[
-3x + 3 = 2x - 7
\]

Now, we will solve for \( x \):

1. Add \( 3x \) to both sides:

\[
3 = 5x - 7
\]

2. Next, add \( 7 \) to both sides:

\[
10 = 5x
\]

3. Now, divide both sides by \( 5 \):

\[
x = 2
\]

Now that we have \( x \), we can substitute it back into either of the original equations to find \( y \). We'll use the first equation \( y = -3x + 3 \):

\[
y = -3(2) + 3
\]
\[
y = -6 + 3
\]
\[
y = -3
\]

Thus, the solution to the system of equations is \( (2, -3) \).

So, the correct response is:

**(2,−3)**