Question

$$y leq \frac{1}{3}x - 1$$
$$y leq \frac{1}{3}x - 3$$
\bigcirc all values that satisfy $y \leq \frac{1}{3}x - 1$ are solutions.
\bigcirc all values that satisfy $y \leq \frac{1}{3}x - 3$ are solutions.
\bigcirc all values that satisfy either $y \leq \frac{1}{3}x - 1$ or $y \leq \frac{1}{3}x - 3$ are solutions.
\bigcirc there are no solutions.

Explanation:

The system is an OR compound inequality (implied by the separate shaded regions for each inequality). A solution to an OR system is any point that satisfies at least one of the inequalities. The graph shows two shaded areas: one for $y \leq \frac{1}{3}x - 1$ (blue) and one for $y \leq \frac{1}{3}x - 3$ (red). Any point in either shaded region is a valid solution.

Answer:

All values that satisfy either $y \leq \frac{1}{3}x - 1$ or $y \leq \frac{1}{3}x - 3$ are solutions.