Which graph represents the solution set of the system of inequalities?

Well first we need to change the format of the equations to slope-intercept, or y=mx+b.
So the first one (x + y < 1) will be changed to   y < -x + 1.
The second one (2y ≥ x - 4) will be changed to   y ≥ x/2 - 2.
Now we can analyze each graph.
In every single graph the first equation (y < -x + 1) is graphed correctly.
Now for the second equation, we can see that only the first and last graph correctly format to the equation.
Now for the shading:
The first equation shows us that y is less than -x +1, making the shading go under the dotted line. (to the left)
The second equation shows us that y is greater than or equal to x/2 - 2, making the shading go above the line. (also to the left)
Therefore, when we shade, the overlapping shading is correctly formatted in the first graph.
Hope this helped, comment any questions you have for me.