Answer:
(2,0) , (4,-20) and (-1,-1)
Step-by-step explanation:
[tex]4x+y>-6[/tex]
WE need to select an ordered pair that is solution to our inequality
Lets check with each option
(2,0) , plug in 2 for x and 0 for y
[tex]4x+y>-6[/tex]
[tex]4(2)+0>-6[/tex]
[tex]8>-6[/tex] True
(−3, 6), plug in -3 for x and 6 for y
[tex]4x+y>-6[/tex]
[tex]4(-3)+6>-6[/tex]
[tex]-6>-6[/tex] False
(4, −20) , plug in 4 for x and -20 for y
[tex]4x+y>-6[/tex]
[tex]4(4)-20>-6[/tex]
[tex]-4>-6[/tex] True
(0, −9) , plug in 0 for x and -9 for y
[tex]4x+y>-6[/tex]
[tex]4(0)-9>-6[/tex]
[tex]-9>-6[/tex] False
(-1, −1) , plug in -1 for x and -1 for y
[tex]4x+y>-6[/tex]
[tex]4(-1)-1>-6[/tex]
[tex]-5>-6[/tex] True
Replacing each ordered pair into the inequality and verifying if it forms an identity, we have that those which is a solution is:
(2,0)
The inequality is:
[tex]4x + y \geq 6[/tex]
Ordered pair (2,0)
[tex]4(2) + 0 \geq 6 \rightarrow 8 \geq 6[/tex]
It is a solution.
Ordered pair (-3,6)
[tex]4(-3) + 6 \geq 6 \rightarrow -6 \geq 6[/tex]
It is not a solution.
Ordered pair (4,-20)
[tex]4(4) - 20 \geq 6 \rightarrow -4 \geq 6[/tex]
It is not a solution.
Ordered pair (0,-9)
[tex]4(0) - 9 \geq 6 \rightarrow -9 \geq 6[/tex]
It is not a solution.
Ordered pair (-1,-1)
[tex]4(-1) - 1 \geq 6 \rightarrow -5 \geq 6[/tex]
It is not a solution.
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