Final answer:
The correct answer is option b: all values that satisfy y < ⅓ x − 3 are solutions to the system of inequalities, as this region encompasses all solutions to y < ⅓ x − 1 as well.
Step-by-step explanation:
The system of inequalities is given by:
y ≤ ⅓ x − 1
y ≤ ⅓ x − 3
To determine which statement is true about the solution to the system of inequalities, we must consider the area on the graph that satisfies both inequalities simultaneously. The solution to this system is the intersection of the two sets of points that satisfy each inequality individually.
If you graph these inequalities, you'd find that the shaded region for the inequality y ≤ ⅓ x − 1 lies below and on the line y = ⅓ x − 1, and similarly for y ≤ ⅓ x − 3. Because the second inequality yawns a region further down on the y-axis (since -3 is less than -1), effectively, all values that satisfy y ≤ ⅓ x − 1 will also satisfy y ≤ ⅓ x − 3. Hence, the correct statement is that all values that satisfy the first inequality are solutions to the system.
This corresponds to option b: All values that satisfy y < ⅓ x − 3 are solutions to the system of inequalities.