Answer:
(8,2)
Explanation:
Given the system of inequalities:
[tex]\begin{gathered} y>\frac{1}{3}x-5 \\ y>-x+3 \end{gathered}[/tex]
First, we determine the x and y-intercepts of each inequality to plot the boundary line.
[tex]\begin{gathered} y=\frac{1}{3}x-5 \\ \text{When x=0,y=-5}\implies(0,-5) \\ \text{When y=0} \\ \frac{1}{3}x=5 \\ x=15\implies(15,0) \end{gathered}[/tex]
Since we have the greater than sign, shade above the boundary line.
For the second inequality:
[tex]\begin{gathered} y>-x+3 \\ \text{Boundary Line:}y=-x+3 \\ \text{When x=0,y=3}\implies(0,3) \\ \text{When y=0,x=3}\implies(3,0) \end{gathered}[/tex]
Since we have the greater than sign, shade above the boundary line.
Any point in the region where the two graphs intersect (shaded purple) is a solution to the system of inequalities.
• One point is (8,2).
You can pick as many points as possible.
