Determine which ordered pairs given are solutions of the linear inequality in two variables.

[tex]\[ x - y \ \textgreater \ 7 \][/tex]

Ordered pairs: [tex]\((6, -1), (9, 1)\)[/tex]

Is the ordered pair [tex]\((6, -1)\)[/tex] a solution to the inequality?

A. No

B. Yes



Answer :

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.