Question
Which statements are true about the ordered pair (2, 3)
and the system of equations?
3x+4y=182x−2y=2
Select each correct answer.
The ordered pair (2, 3)
is not a solution to the system of linear equations.
The ordered pair begin ordered pair 2 comma 3 end ordered pair is not a solution to the system of linear equations.
When (2, 3)
is substituted into the second equation, the equation is false.
When begin ordered pair 2 comma 3 end ordered pair is substituted into the second equation, the equation is false.
When (2, 3)
is substituted into the first equation, the equation is false.
When begin ordered pair 2 comma 3 end ordered pair is substituted into the first equation, the equation is false.
When (2, 3)
is substituted into the second equation, the equation is true.
When begin ordered pair 2 comma 3 end ordered pair is substituted into the second equation, the equation is true.
The ordered pair (2, 3)
is a solution to the system of linear equations.
The ordered pair begin ordered pair 2 comma 3 end ordered pair is a solution to the system of linear equations.
When (2, 3)
is substituted into the first equation, the equation is true.
and the system of equations?
3x+4y=182x−2y=2
Select each correct answer.
The ordered pair (2, 3)
is not a solution to the system of linear equations.
The ordered pair begin ordered pair 2 comma 3 end ordered pair is not a solution to the system of linear equations.
When (2, 3)
is substituted into the second equation, the equation is false.
When begin ordered pair 2 comma 3 end ordered pair is substituted into the second equation, the equation is false.
When (2, 3)
is substituted into the first equation, the equation is false.
When begin ordered pair 2 comma 3 end ordered pair is substituted into the first equation, the equation is false.
When (2, 3)
is substituted into the second equation, the equation is true.
When begin ordered pair 2 comma 3 end ordered pair is substituted into the second equation, the equation is true.
The ordered pair (2, 3)
is a solution to the system of linear equations.
The ordered pair begin ordered pair 2 comma 3 end ordered pair is a solution to the system of linear equations.
When (2, 3)
is substituted into the first equation, the equation is true.
Answers
GPT-4o mini
To determine which statements are true about the ordered pair (2, 3) and the system of equations, we need to substitute \( x = 2 \) and \( y = 3 \) into both equations:
1. The first equation is \( 3x + 4y = 18 \).
Substituting in the values:
\[
3(2) + 4(3) = 6 + 12 = 18
\]
This is true.
2. The second equation is \( 2x - 2y = 2 \).
Substituting in the values:
\[
2(2) - 2(3) = 4 - 6 = -2
\]
This is false.
Based on this analysis, we can evaluate the statements:
1. **The ordered pair (2, 3) is not a solution to the system of linear equations.**
- **True** (because it does not satisfy both equations)
2. **When (2, 3) is substituted into the second equation, the equation is false.**
- **True** (the second equation does not hold)
3. **When (2, 3) is substituted into the first equation, the equation is false.**
- **False** (the first equation holds true)
4. **When (2, 3) is substituted into the second equation, the equation is true.**
- **False** (the second equation does not hold)
5. **The ordered pair (2, 3) is a solution to the system of linear equations.**
- **False** (it does not satisfy both equations)
6. **When (2, 3) is substituted into the first equation, the equation is true.**
- **True** (the first equation is satisfied)
Therefore, the true statements are:
- The ordered pair (2, 3) is not a solution to the system of linear equations.
- When (2, 3) is substituted into the second equation, the equation is false.
- When (2, 3) is substituted into the first equation, the equation is true.
1. The first equation is \( 3x + 4y = 18 \).
Substituting in the values:
\[
3(2) + 4(3) = 6 + 12 = 18
\]
This is true.
2. The second equation is \( 2x - 2y = 2 \).
Substituting in the values:
\[
2(2) - 2(3) = 4 - 6 = -2
\]
This is false.
Based on this analysis, we can evaluate the statements:
1. **The ordered pair (2, 3) is not a solution to the system of linear equations.**
- **True** (because it does not satisfy both equations)
2. **When (2, 3) is substituted into the second equation, the equation is false.**
- **True** (the second equation does not hold)
3. **When (2, 3) is substituted into the first equation, the equation is false.**
- **False** (the first equation holds true)
4. **When (2, 3) is substituted into the second equation, the equation is true.**
- **False** (the second equation does not hold)
5. **The ordered pair (2, 3) is a solution to the system of linear equations.**
- **False** (it does not satisfy both equations)
6. **When (2, 3) is substituted into the first equation, the equation is true.**
- **True** (the first equation is satisfied)
Therefore, the true statements are:
- The ordered pair (2, 3) is not a solution to the system of linear equations.
- When (2, 3) is substituted into the second equation, the equation is false.
- When (2, 3) is substituted into the first equation, the equation is true.