Answer:
The system of inequalities is
[tex]y\leq -\frac{1}{3}x+2[/tex]
[tex]y>\frac{2}{3}x+3[/tex]
Step-by-step explanation:
step 1
Find the equation of the solid red line
Let
[tex]A(0,2),B(3,1)[/tex]
Find the slope
[tex]m=(1-2)/(3-0)=-1/3[/tex]
The equation of the line is
[tex]y=-\frac{1}{3}x+2[/tex]
The solution of the inequality is the shaded area below the solid red line
therefore
The inequality is
[tex]y\leq -\frac{1}{3}x+2[/tex]
step 2
Find the equation of the dashed blue line
Let
[tex]A(0,3),B(3,5)[/tex]
Find the slope
[tex]m=(5-3)/(3-0)=2/3[/tex]
The equation of the line is
[tex]y=\frac{2}{3}x+3[/tex]
The solution of the inequality is the shaded area above the dashed blue line
therefore
The inequality is
[tex]y>\frac{2}{3}x+3[/tex]
The system of inequalities is
[tex]y\leq -\frac{1}{3}x+2[/tex]
[tex]y>\frac{2}{3}x+3[/tex]
