Question

Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y ≥ - x + 3y > 2x - 6LABEL ALL COORDINATES

Answer 1

The inequalities are given below as

`\begin{gathered} y\ge-x+3 \\ y>2x-6 \end{gathered}`

Step 1:

Calculate the x-intercept by putting y=0

`\begin{gathered} y=-x+3 \\ 0=-x+3 \\ x=3 \\ (3,0) \end{gathered}`

Calculate the y-intercept by putting x=0

`\begin{gathered} y=-x+3 \\ y=-0+3 \\ y=3 \\ (0,3) \end{gathered}`

The graph is given below as

Step 2:

Calculate the x-intercept by putting y=0

`\begin{gathered} y=2x-6 \\ 0=2x-6 \\ 2x=6 \\ (2x)/(2)=(6)/(2) \\ x=3 \\ (3,0) \end{gathered}`

Calculate the y-intercept by putting x=0

`\begin{gathered} y=2x-6 \\ y=2(0)-6 \\ y=0-6 \\ y=-6 \\ (0,-6) \end{gathered}`

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)