Solve the following systems of inequalities and select the correct graph:

2x − y < 4
x + y > −1

In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB.

The graph of 2x - y < 4 is shown in figure 1. We graph 2x-y = 4 through the two points (0,-4) and (2,0) and shade above the dashed line. Points on the dashed line do not count as solutions.

The graph of x+y > -1 is shown in figure 2. This boundary line x+y = -1 goes through (-1,0) and (0,-1). The boundary line is also dashed.

Combine the graphs of figure 1 and figure 2. Specifically look where they overlap. Figure 3 has both graphs on the same xy coordinate system. The green region is where the yellow and blue overlap, or mix so to speak. The green region represents the set of all (x,y) points that make both original inequalities to be true.

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