Which of the following ordered pairs are solutions to the system of
inequalities? Check all that apply.
2x < y
y>7
O A. (8,2)
O B. (0,0)
O C. (5,5)
O D. (1,9)
O E. (17,50)
OF. (-1, 10)
Answers
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.
Option A: (8, 2)[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.
Option B: (0, 0)[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.
Option C: (5, 5)[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.
Option D: (1, 9)[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.
Option E: (17, 50)[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.
Option F: (-1, 10)[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.
Final Answer:Therefore, Options D, E, and F are the solutions to the given system of linear inequalities.
___________________________Keywords:Linear Inequalities in two variables
System of linear inequalities
________________________________
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#1
Passes through
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Step-by-step explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
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Step 1:
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Let's solve your system by elimination.
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Step-by-step explanation:
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Step-by-step explanation:
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Considering the given focus and directrix, the equation of the parabola is given by:
[tex]y = -2.375x^2[/tex]
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Thus the equation of the parabola is given by:
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