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.

Answer 1

To determine which statement about the ordered pair \((1, -7)\) is true, we need to substitute \(x = 1\) and \(y = -7\) into both equations and check if they hold true.

1. **First equation**: \(y = -3x - 4\)

Substitute \(x = 1\) and \(y = -7\):
\[
-7 = -3(1) - 4
\]
\[
-7 = -3 - 4
\]
\[
-7 = -7 \quad \text{(True)}
\]

2. **Second equation**: \(-9x - 3y = -2\)

Substitute \(x = 1\) and \(y = -7\):
\[
-9(1) - 3(-7) = -2
\]
\[
-9 + 21 = -2
\]
\[
12 \neq -2 \quad \text{(False)}
\]

Based on this analysis:
- The ordered pair \((1, -7)\) is a solution to the first equation but not to the second equation.

Thus the correct response is:

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