Which graph represents the solution to the system of inequalities?
x + y ≤ 50
x ≥ 20

Consider the inequality x+y≤50, that is y≤-x+50

we first draw the line y=-x+50, using the x and y intercepts:

(50, 0) and (0, 50). To check which region to color, we pick any point, for example (0, 25). for this point the inequality 25≤-0+50 is true, so we have picked a point in the region that we will color. (we color it with yellow as shown in the picture)

consider x ≥ 20. This inequality represents all vertical lines starting at x=20, and to the right of this line. So we color the region to the right of x=20. (colored with light gray)

The solution of the inequality system is the intersection of both regions, that is the region which is colored with both colors.

Solution: the purple region