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 > -2x - 2\\
\\y \ge x - 8\\

Explanation:

Graph the first inequality

Using the Graphing Linear Inequalities knowledge point

$$
LATEXBLOCK0
$$

Graph the second inequality

Using the Graphing Linear Inequalities knowledge point

$$
LATEXBLOCK1
$$

Find the intersection and a solution point

Using the Systems of Linear Inequalities knowledge point

$$
LATEXBLOCK2
$$

Answer:

The system of inequalities is solved graphically by plotting the boundary lines and shading the appropriate regions:

1. For \(y > -2x - 2\), graph the dashed boundary line \(y = -2x - 2\) and shade the region above it.
2. For \(y \ge x - 8\), graph the solid boundary line \(y = x - 8\) and shade the region above and including the line.

The solution set is the overlapping region of these two shaded areas.

A point in the solution set is \((3, 0)\).