we will proceed to resolve each case to determine the solution
we have
[tex]2x+y>-4[/tex]
[tex]y>-2x-4[/tex]
we know that
If an ordered pair is the solution of the inequality, then it must satisfy the inequality.
case a) [tex](5,-12)[/tex]
Substitute the value of x and y in the inequality
[tex]-12>-2*5-4[/tex]
[tex]-12>-14[/tex] ------> is True
therefore
the ordered pair [tex](5,-12)[/tex] is a solution of the inequality
case b) [tex](-3,0)[/tex]
Substitute the value of x and y in the inequality
[tex]0>-2*-3-4[/tex]
[tex]0>2[/tex] ------> is False
therefore
the ordered pair [tex](-3,0)[/tex] is not a solution of the inequality
case c) [tex](-1,-1)[/tex]
Substitute the value of x and y in the inequality
[tex]-1>-2*-1-4[/tex]
[tex]-1>-2[/tex] ------> is True
therefore
the ordered pair[tex](-1,-1)[/tex] is a solution of the inequality
case d) [tex](0,1)[/tex]
Substitute the value of x and y in the inequality
[tex]1>-2*0-4[/tex]
[tex]1>-4[/tex] ------> is True
therefore
the ordered pair [tex](0,1)[/tex] is a solution of the inequality
case e) [tex](4,-12)[/tex]
Substitute the value of x and y in the inequality
[tex]-12>-2*4-4[/tex]
[tex]-12>-12[/tex] ------> is False
therefore
the ordered pair [tex](4,-12)[/tex] is not a solution of the inequality
Verify
using a graphing tool
see the attached figure
the solution is the shaded area above the line
The points A,C, and D lies on the shaded area, therefore the ordered pairs A,C, and D are solution of the inequality
