Question

Solve the system of linear inequality by graphing and label the solution region.

Answer 1

You need to remember that the equation of a line in Slope-Intercept form, is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

In this case, you have the first line:

`y=(2)/(3)x+3`

So you can identify that:

`\begin{gathered} m_1=(2)/(3) \\ \\ b_1=3 \end{gathered}`

The second line is:

`y=-(4)/(3)x-3`

Where:

`\begin{gathered} m_2=-(4)/(3) \\ \\ b_2=-3 \end{gathered}`

Notice that the first inequality has this symbol:

`\ge`

That means that the line is solid and the shaded region is above the line.

The second inequality has this symbol:

`>`

That means that the second line must be dashed and the shaded region is above the line.

Knowing the above, you can graph the System of linear inequalities.

The answer is: