Answer-
First graph represents the system of linear inequalities.
Solution-
The system of linear inequalities are,
[tex]y<3x+1\\\\y\geq-2x-4[/tex]
Considering them as equalities,
[tex]y=3x+1[/tex] ---------------1
[tex]y=-2x-4[/tex] -----------2
Subtracting both equations,
[tex]\Rightarrow 0=3x+1+2x+4[/tex]
[tex]\Rightarrow 5x+5=0[/tex]
[tex]\Rightarrow 5x=-5[/tex]
[tex]\Rightarrow x=-1[/tex]
Putting the value of x in equation 1,
[tex]y=3(-1)+1=-2[/tex]
So, the point of intersection is (-1, -2)
Taking the point as origin and putting it in inequality 1,
[tex]\Rightarrow 0<3(0)+1[/tex]
[tex]\Rightarrow 0<1[/tex]
As it satisfies, so the shaded region will be towards origin.
Taking the point as origin and putting it in inequality 2,
[tex]\Rightarrow 0\geq-2(0)-4[/tex]
[tex]\Rightarrow 0\geq-4[/tex]
As it satisfies, so the shaded region will be towards origin.
From above, option has the correct graph.
