Final answer:
Find the graph that displays y = -2x as a solid line with shading below and y = 3x - 4 as a dashed line with shading above. The intersection of these shadings represents the solution to the system of inequalities.
Step-by-step explanation:
The question involves finding which graph represents the solution to a system of inequalities. The system given is:
To find the graph representing the solution:
- Firstly, graph the line y = -2x. Since the inequality is ≤, this line will be solid, and shading will be below the line, as the y-values are less than or equal to the line's y-values.
- Next, graph the line y = 3x - 4. As the inequality is >, this line will be dashed to indicate that points on the line are not included in the solution, and the shading will be above the line because y-values are greater than the y-values on the line.
- The region of intersection where the shadings overlap is the solution to the system.
The correct graph will show both inequalities with the respective shadings and a clear intersection of shaded areas.