Respuesta :
Answer:
Option 3.
Step-by-step explanation:
The given inequalities are
[tex]x-2y<4[/tex]
[tex]y>-2x-5[/tex]
If (a,b) is solution of given system of inequalities, then the above inequalities must be satisfy by the point (a,b).
For point (1,-4),
[tex](1)-2(-4)<4\Rightarrow 9<4[/tex] False
[tex]-4>-2(1)-5\Rightarrow -4>-7[/tex] True
Since, first inequality is false for (1,-4) point, therefore (1,-4) is not the solution.
For point (-8,2),
[tex](-8)-2(2)<4\Rightarrow -12<4[/tex] True
[tex]2>-2(-8)-5\Rightarrow 2>11[/tex] False
Since, second inequality is false for (-8,2) point, therefore (-8,2) is not the solution.
For point (0,0),
[tex](0)-2(0)<4\Rightarrow 0<4[/tex] True
[tex]0>-2(0)-5\Rightarrow 0>-5[/tex] True
Since, both of inequalities are true, therefore (0,0) is a the solution.
For point (-3,0),
[tex](-3)-2(0)<4\Rightarrow -3<4[/tex] True
[tex]0>-2(-3)-5\Rightarrow 0>-11[/tex] False
Since, second inequality is false for (-3,0) point, therefore (-3,0) is not the solution.
Hence, option 3 is correct.
