Question

Consider the system of equations:

y=−2x+4


y=−13x−1


The solution is (3, −2)
. When verifying the solution, what does your final step look like?

(1 point)
Responses

−3=−3
negative 3 is equal to negative 3

4=4
4 is equal to 4

−1=−1
negative 1 is equal to negative 1

−2=−2

Answer 1

To verify the solution (3, −2) for the system of equations, you need to substitute \( x = 3 \) and \( y = -2 \) into both equations and check if they hold true.

1. For the first equation \( y = -2x + 4 \):

Substituting \( x = 3 \):
\[
y = -2(3) + 4 = -6 + 4 = -2
\]
This gives \( -2 = -2 \), which is true.

2. For the second equation \( y = -13x - 1 \):

Substituting \( x = 3 \):
\[
y = -13(3) - 1 = -39 - 1 = -40
\]
This gives \( -2 = -40 \), which is false.

Since the values do not satisfy the second equation, the solution is incorrect. The correct final step of verification, assuming you wanted to verify the first equation, would be:

\[
-2 = -2
\]
So, the response that matches the validation of the first equation is:

**−2=−2** (negative 2 is equal to negative 2)