Answer:
The graph for the following system of inequalities is attached below.
Step-by-step explanation:
The given system of inequalities is
[tex]x+y>3[/tex] .... (1)
[tex]x+y<-4[/tex] .... (2)
From inequality (1) and (2) it is clear that (x+y) is greater than 3 adn 3 is not less than -4. So, the given system of inequality has no feasible reason or solution.
The related equation of first inequality is
[tex]x+y=3[/tex]
Put x=0 to find the y-intercept.
[tex]0+y=3\Rightarrow y=3[/tex]
The y-intercept is 3.
Put y=0 to find the x-intercept.
[tex]x+0=3\Rightarrow x=3[/tex]
The x-intercept is 3.
The related equation of second inequality is
[tex]x+y=-4[/tex]
Put x=0 to find the y-intercept.
[tex]0+y=-4\Rightarrow y=-4[/tex]
The y-intercept is -4.
Put y=0 to find the x-intercept.
[tex]x+0=-4\Rightarrow x=-4[/tex]
The x-intercept is -4.
The related lines are dotted line because the sign of inequalities are > and <.
Check each inequality be (0,0).
[tex]0+0>3[/tex]
[tex]0>3[/tex]
This statement is false. So the shaded region of first inequality is opposite sides of the origin.
[tex]0+0<-4[/tex]
[tex]0<-4[/tex]
This statement is false. So the shaded region of first inequality is opposite sides of the origin.
The graph for the following system of inequalities is attached below.
