The graph shows the solution to which system of inequalities? a) y < x + 1 and y < x - 3 b) y ≤ x + 1 and y > x - 3 c) y ≤ x + 1 and y ≤ x - 3 d) y ≤ x + 1 and y ≥ x - 3

 
b. y ≤ x + 1 and y > x - 3

Explanation:
First of all, remember that a solid line means the inequality has a ≤ or ≥ sign, and a dotted line means the inequality has a < or > sign.
One way to solve this is to find a point inside the shaded region, like (0, 0) that you can test in the options to see which ones work. Another method is to figure out what the graph of each line is and then make sure the signs are turned the right direction so the shading is correct. 
We know that the first inequality should have a greater/less than or equal to sign because the line is solid and the second inequality should just be a greater/less than sign because the line is dotted. That means it has to be B, because this is the only correct combination of signs. 
But to be sure, you should check. Try (-1,0) and (0, 0)
y ≤ x + 1   and  y > x - 3
0 ≤ -1 + 1         0 > - 1 - 3
0 ≤ 0 yes         0 > - 4 yes 

0 ≤ 0 + 1          0 > 0 - 3
0 ≤ 1 yes         0 > -3  yes