Final answer:
The solution to the system of inequalities y < -4/3x - 3 and y <= -x + 3 is the region below the line y = -4/3x - 3 and below or on the line y = -x + 3.
Step-by-step explanation:
To solve the system of inequalities:
y < -4/3x - 3
y <= -x + 3
We can start by graphing the boundary lines.
For the equation y = -4/3x - 3, we plot the y-intercept at (0, -3) and use the slope to find additional points.
For the equation y = -x + 3, we plot the y-intercept at (0, 3) and use the slope to find additional points.
Since the inequality sign is < or <=, the lines should be drawn with dashed lines to indicate that the points on the lines are not included in the solution set.
Next, we shade the region below the line y = -4/3x - 3 and the region below or on the line y = -x + 3. The solution to the system of inequalities is the intersection of the shaded regions.
In this case, the solution set is the region below the line y = -4/3x - 3 and below or on the line y = -x + 3.
In summary, the solution to the system of inequalities y < -4/3x - 3 and y <= -x + 3 is the region below the line y = -4/3x - 3 and below or on the line y = -x + 3.