Question

A system of equations is shown below.

y = -3x – 4

-9x – 3y = -2

Which statement about the ordered pair (1, -7) is true?
Responses
A It is not a solution to either equation.It is not a solution to either equation.
B It is the only solution to the system. It is the only solution to the system.
C It is one of many solutions to the system.It is one of many solutions to the system.
D It is a solution to the first but not the second equation.It is a solution to the first but not the second equation.

Answer 1

To determine which statement about the ordered pair (1, -7) is true, we will substitute \( x = 1 \) and \( y = -7 \) into both equations.

1. **Substituting into the first equation:**

\[
y = -3x - 4
\]

Substituting \( x = 1 \):

\[
-7 = -3(1) - 4
\]
\[
-7 = -3 - 4
\]
\[
-7 = -7
\]

This equation is true.

2. **Substituting into the second equation:**

\[
-9x - 3y = -2
\]

Substituting \( x = 1 \) and \( y = -7 \):

\[
-9(1) - 3(-7) = -2
\]
\[
-9 + 21 = -2
\]
\[
12 \neq -2
\]

This equation is false.

From the calculations, the ordered pair (1, -7) is a solution to the first equation but not the second one.

Therefore, the correct statement is:

**D: It is a solution to the first but not the second equation.**