Solve the system by graphing:

$\left\{\begin{array}{l}y\ge 3x+1\\ -3x+y\ge -4\end{array}\right.$

The given system of inequalities are:

$\left\{\begin{array}{l}y\ge 3x+1\\ -3x+y\ge -4\end{array}\right.$

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 $y\ge 3x+1$

$$\begin{gathered} y\ge 3x+1 \\ 5\ge 3\times 0+1 \\ 5\ge 1 \end{gathered}$$

This is true

For inequality $-3x+y\ge -4$

$$\begin{gathered} -3x+y\ge -4 \\ -3\times 0+5\ge -4 \\ 5\ge 4 \end{gathered}$$

This is true.

Thus, the solution set is correct.