91Ó°ÊÓ

The given system of inequalities are:

$\left\{\begin{array}{l}yâ‰\yen 3x+1\\ −3x+yâ‰\yen −4\end{array}\right.$

We will graph the inequality by graphing $y=3x+2$and the boundary will be a solid line because it contains greater than equal to sign.

The graph is given as:

We will graph the inequality by graphing $−3x+y=−4$on the same cartesian plane and the boundary will be a solid line because it contains greater than equal to sign.

The graph is given as:

The solution of the given system of inequalities is the common region between inequalities represented by the dark region (dark blue) in the above graph.

Substitute the ordered pair $\left(0,5\right)$in both equalities as it is in the solution region.

For inequality $yâ‰\yen 3x+1$

$$\begin{gathered} yâ‰\yen 3x+1 \\ 5â‰\yen 3×0+1 \\ 5â‰\yen 1 \end{gathered}$$

This is true

For inequality $-3x+yâ‰\yen -4$

$$\begin{gathered} -3x+yâ‰\yen -4 \\ -3×0+5â‰\yen -4 \\ 5â‰\yen 4 \end{gathered}$$

This is true.

Thus, the solution set is correct.