Answer:
Options D, E, F
Step-by-step explanation:
Given the following system of linear inequalities in two variables:
[tex]\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}[/tex]
We can substitute the given ordered pairs to see whether they satisfy both linear inequalities.
[tex]\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}[/tex]
2x < y
⇒ 2(8) < 2
⇒ 16 < 2 (False statement).
y > 7
⇒ 2 > 7 (False statement).
⇒ (8, 2) is not a solution to the system.
[tex]\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}[/tex]
2x < y
⇒ 2(0) < 2
⇒ 0 < 2 (True statement).
y > 7
⇒ 0 > 7 (False statement).
⇒ (0, 0) is not a solution to the system.
[tex]\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}[/tex]
2x < y
⇒ 2(5) < 5
⇒ 10 < 2 (False statement).
y > 7
⇒ 5 > 7 (False statement).
⇒ (5, 5) is not a solution to the system.
[tex]\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}[/tex]
2x < y
⇒ 2(1) < 9
⇒ 2 < 9 (True statement).
y > 7
⇒ 9 > 7 (True statement).
⇒ (1, 9) is a solution to the system.
[tex]\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}[/tex]
2x < y
⇒ 2(17) < 50
⇒ 34 < 50 (True statement).
y > 7
⇒ 50 > 7 (True statement).
⇒ (17, 50) is also a solution to the system.
[tex]\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}[/tex]
2x < y
⇒ 2(-1) < 10
⇒ -2 < 10 (True statement).
y > 7
⇒ 10 > 7 (True statement).
⇒ (-1, 10) is also a solution to the system.
Therefore, Options D, E, and F are the solutions to the given system of linear inequalities.
Linear Inequalities in two variables
System of linear inequalities
________________________________
Learn more about system of linear inequalities here:
https://brainly.com/question/9774970
