Final answer:
To graph the solution to the system of inequalities, graph each inequality separately and shade the region that satisfies both inequalities.
Step-by-step explanation:
To graph the solution to the system of inequalities, we need to graph each inequality separately and shade the region that satisfies both inequalities. Let's start with the first inequality, -5x + 6y ≥ 18:
Step 1: Rewrite the inequality in slope-intercept form (y = mx + b) by solving for y:
y ≥ (5/6)x + 3
Step 2: Graph the boundary line y = (5/6)x + 3 as a solid line (since it is ≥ and not >).
Step 3: Shade the region above the line, including the line itself, since y is greater than or equal to (5/6)x + 3.
Next, let's graph the second inequality, x > -2:
Step 1: Graph the vertical line x = -2 as a dashed line (since it is > and not ≥).
Step 2: Shade the region to the right of the line, excluding the line itself, since x is greater than -2.
The shaded region that satisfies both inequalities is the solution to the system of inequalities.