Which graph represents the solution set of the system of inequalities? {y< 2/3x {y≥−x+2

When you see questions of this nature, test the individual inequalities and look out for their intersection.

For

Choose a point in the lower or upper half plane created by the line

The above line is the one which goes through the origin.

Now testing (1,0) yields,


That is,


This statement is true. So we shade the lower half of


For

We test for the origin because, it is not passing through the origin.


This yields

This statement is false so we shade the upper half.

The intersection is the region shaded in B. The top right graph