Question
What ordered pair is the solution to y > 2x and y > 7
Answers
Answered by
GPT-4o mini
To find an ordered pair that satisfies the inequalities \( y > 2x \) and \( y > 7 \), we can start by choosing a value for \( y \) such that it is greater than 7. For example, let’s select \( y = 8 \).
Next, we need to satisfy the first inequality \( y > 2x \):
\[ 8 > 2x \]
To find \( x \), we can rearrange this inequality:
\[ 2x < 8 \]
Dividing both sides by 2 gives us:
\[ x < 4 \]
Now we can choose a value for \( x \) that is less than 4. Let's pick \( x = 3 \).
Now we have the ordered pair \( (3, 8) \).
To verify, we check both inequalities:
1. **For \( y > 2x \)**:
\[
8 > 2(3) \\
8 > 6 \quad \text{(true)}
\]
2. **For \( y > 7 \)**:
\[
8 > 7 \quad \text{(true)}
\]
Thus, the ordered pair \( (3, 8) \) satisfies both inequalities.
Another example could be \( (0, 8) \) or \( (4, 9) \), as long as \( x < 4 \) and \( y > 7 \).
In conclusion, one valid ordered pair solution is \( (3, 8) \).
Next, we need to satisfy the first inequality \( y > 2x \):
\[ 8 > 2x \]
To find \( x \), we can rearrange this inequality:
\[ 2x < 8 \]
Dividing both sides by 2 gives us:
\[ x < 4 \]
Now we can choose a value for \( x \) that is less than 4. Let's pick \( x = 3 \).
Now we have the ordered pair \( (3, 8) \).
To verify, we check both inequalities:
1. **For \( y > 2x \)**:
\[
8 > 2(3) \\
8 > 6 \quad \text{(true)}
\]
2. **For \( y > 7 \)**:
\[
8 > 7 \quad \text{(true)}
\]
Thus, the ordered pair \( (3, 8) \) satisfies both inequalities.
Another example could be \( (0, 8) \) or \( (4, 9) \), as long as \( x < 4 \) and \( y > 7 \).
In conclusion, one valid ordered pair solution is \( (3, 8) \).