Final answer:
To find which ordered pairs satisfy both inequalities, we can graph the lines and shade the region that satisfies both inequalities. The shaded region represents the ordered pairs (x, y) that satisfy both 2x + 7y > 5 and 3x - y < 2.
Step-by-step explanation:
To find which ordered pairs satisfy both inequalities, we can graph the lines and shade the region that satisfies both inequalities. Let's start by graphing the lines 2x + 7y > 5 and 3x - y < 2 individually.
First, let's graph the line 2x + 7y = 5. To do this, we need to find two points on the line. Let's choose x = 0 as one point. Plugging in x = 0 into the equation, we get 7y = 5, and solving for y gives us y = 5/7. For the second point, let's choose y = 0. Plugging in y = 0 into the equation, we get 2x = 5, and solving for x gives us x = 5/2.
Next, let's graph the line 3x - y = 2. Using the same method, we find that one point is (0, -2/3) and another point is (2/3, 0).
Now, we can shade the region that satisfies both inequalities. The shaded region represents the ordered pairs (x, y) that satisfy both 2x + 7y > 5 and 3x - y < 2. Any ordered pairs in this region would satisfy both inequalities.