Answer:
The graph of given inequalities is shown below.
Step-by-step explanation:
The given linear inequalities are
[tex]3x+y>1[/tex]
[tex]y\leq x+2[/tex]
The related equations for given inequalities are
[tex]3x+y=1[/tex]
[tex]y=x+2[/tex]
First of all find the x and y-intercepts of the above equations.
[tex]3(0)+y=1\Rightarrow y=1[/tex]
[tex]3x+(0)=1\Rightarrow x=\frac{1}{3}[/tex]
The y-intercept is (0,1) and x-intercept is [tex](\frac{1}{3},0)[/tex].
[tex]y=0+2\Rightarrow y=2[/tex]
[tex]0=x+2\Rightarrow x=-2[/tex]
The y-intercept is (0,2) and x-intercept is (-2,0).
Now, check the iniquities by (0,0).
[tex]3(0)+(0)>1[/tex]
[tex]0>1[/tex]
This statement is not true, so the shaded region of first inequality is opposite to the origin. The related line is a dashed line because the side of inequality is >.
[tex]0\leq 0+2[/tex]
[tex]0\leq 2[/tex]
This statement is true, so the shaded region of second inequality is towards the origin.The related line is a solid line because the side of inequality is ≤.
