Answer:
The graph of system of inequalities is shown below.
Step-by-step explanation:
The given inequalities are
[tex]y<2x-5[/tex]
[tex]y>-3x+1[/tex]
The related equation of the given inequalities are
[tex]y=2x-5[/tex]
[tex]y=-3x+1[/tex]
First find the x-intercept and y-intercepts of related equations.
[tex]y=2(0)-5=-5[/tex]
[tex]0=2x-5\Rightarrow 2.5[/tex]
The x-intercept is (2.5,0) and y-intercept is (0,-5).
[tex]y=-3(0)+1=1[/tex]
[tex]0=-3x+1\Rightarrow 0.333[/tex]
The x-intercept is (0.333,0) and y-intercept is (0,1).
The related line is a doted line because the sign inequalities are > and <.
Check the inequalities by (0,0).
[tex](0)<2(0)-5\Rightarrow 0<-5[/tex]
It is a false statement. So, (0,0) does not contained in shaded region.
[tex]0>-3(0)+1\Rightarrow 0>15[/tex]
It is a false statement. So, (0,0) does not contained in shaded region.
The graph of system of inequalities is shown below.
