Final answer:
To solve the system of inequalities, graph the boundary lines for each inequality and shade the appropriate regions. The solution to the system is the overlapping shaded area on the coordinate plane.
Step-by-step explanation:
To solve the system of inequalities 3y > 2x + 12 and 2x + y ≤ -5, you need to graph each inequality on the coordinate plane and find the region of intersection that satisfies both conditions.
- Start by graphing the inequality 3y > 2x + 12. Convert it to y > (2/3)x + 4 to find the slope and y-intercept. Graph the boundary line y = (2/3)x + 4 and shade above the line since y is greater than the expression.
- Next, graph the inequality 2x + y ≤ -5. Rearrange it to y ≤ -2x - 5. Graph the boundary line y = -2x - 5 and shade below the line since y is less than or equal to the expression.
- The solution to the system of inequalities is the region where the shaded areas of both inequalities overlap on the coordinate plane.