Answer:
The inequalities are given below as
[tex]\begin{gathered} y\ge-x+3 \\ y>2x-6 \end{gathered}[/tex]
Step 1:
Calculate the x-intercept by putting y=0
[tex]\begin{gathered} y=-x+3 \\ 0=-x+3 \\ x=3 \\ (3,0) \end{gathered}[/tex]
Calculate the y-intercept by putting x=0
[tex]\begin{gathered} y=-x+3 \\ y=-0+3 \\ y=3 \\ (0,3) \end{gathered}[/tex]
The graph is given below as
Step 2:
Calculate the x-intercept by putting y=0
[tex]\begin{gathered} y=2x-6 \\ 0=2x-6 \\ 2x=6 \\ \frac{2x}{2}=\frac{6}{2} \\ x=3 \\ (3,0) \end{gathered}[/tex]
Calculate the y-intercept by putting x=0
[tex]\begin{gathered} y=2x-6 \\ y=2(0)-6 \\ y=0-6 \\ y=-6 \\ (0,-6) \end{gathered}[/tex]
The graph is given below as
Combing the two graphs, we will have
Hence,
The coordinate of the point in the solution set will be (3,5)
