To determine whether each ordered pair is a solution to the inequality [tex]\( x - y > 7 \)[/tex], we need to substitute the values of each pair into the inequality and check if the resulting statement is true.
Let's start with the ordered pair [tex]\( (6, -1) \)[/tex]:
1. Substitute [tex]\( x = 6 \)[/tex] and [tex]\( y = -1 \)[/tex] into the inequality [tex]\( x - y > 7 \)[/tex]:
[tex]\[
6 - (-1) > 7
\][/tex]
2. Simplify the expression inside the inequality:
[tex]\[
6 + 1 > 7
\][/tex]
3. Compute the result:
[tex]\[
7 > 7
\][/tex]
Since 7 is not greater than 7, the inequality [tex]\( 6 - (-1) > 7 \)[/tex] is false. Therefore, the ordered pair [tex]\( (6, -1) \)[/tex] is not a solution to the inequality.
Next, consider the ordered pair [tex]\( (9, 1) \)[/tex]:
1. Substitute [tex]\( x = 9 \)[/tex] and [tex]\( y = 1 \)[/tex] into the inequality [tex]\( x - y > 7 \)[/tex]:
[tex]\[
9 - 1 > 7
\][/tex]
2. Simplify the expression inside the inequality:
[tex]\[
8 > 7
\][/tex]
3. Compute the result:
[tex]\[
8 > 7
\][/tex]
Since 8 is indeed greater than 7, the inequality [tex]\( 9 - 1 > 7 \)[/tex] is true. Therefore, the ordered pair [tex]\( (9, 1) \)[/tex] is a solution to the inequality.
So, the final answer to the question is:
Is the ordered pair [tex]\( (6, -1) \)[/tex] a solution to the inequality?
No, it is not.
