Question

Question
Which statements are true about the ordered pair (10, 5) and the system of equations?

{2x−5y=−5x+2y=11


Select each correct answer.



The ordered pair (10, 5) is a solution to the first equation because it makes the first equation true.
The ordered pair begin ordered pair 10 comma 5 end ordered pair is a solution to the first equation because it makes the first equation true.

The ordered pair (10, 5) is a solution to the second equation because it makes the second equation true.
The ordered pair begin ordered pair 10 comma 5 end ordered pair is a solution to the second equation because it makes the second equation true.

The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false.
The ordered pair begin ordered pair 10 comma 5 end ordered pair is not a solution to the system because it makes at least one of the equations false.

The ordered pair (10, 5) is a solution to the system because it makes both equations true.

Answer 1

To determine which statements are true about the ordered pair (10, 5) in relation to the system of equations:

1. **First, let's write down the system of equations clearly**:
- \( 2x - 5y = -5 \)
- \( x + 2y = 11 \)

2. **Now substitute (10, 5) into each equation**:

**For the first equation**:
\[
2(10) - 5(5) = -5
\]
This simplifies to:
\[
20 - 25 = -5
\]
\[
-5 = -5 \quad \text{(True)}
\]

**For the second equation**:
\[
10 + 2(5) = 11
\]
This simplifies to:
\[
10 + 10 = 11
\]
\[
20 = 11 \quad \text{(False)}
\]

3. **Now evaluate the statements**:

- The ordered pair (10, 5) is a solution to the first equation because it makes the first equation true. **(True)**

- The ordered pair (10, 5) is a solution to the second equation because it makes the second equation true. **(False)**

- The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false. **(True)**

- The ordered pair (10, 5) is a solution to the system because it makes both equations true. **(False)**

### Final Answers:
- **The ordered pair (10, 5) is a solution to the first equation because it makes the first equation true.**
- **The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false.**