Graph the system of inequalities:
To graph the system you perform two steps:
(1) Graph the "lines"-- if the inequality is strict (<,>) then the line is dashed, otherwise (`<=,>=)` solid.
(2) Then you must determine the region to shade -- shading indicates every point in the region is a solution to the system.
Since there are two lines that intersect at a point, there will be 4 regions to choose from.
First graph the lines `y=3/2x+3` and `-y=2x` ; both lines will be dashed as no point on either line is a solution to the system. Here the graph of `y=3/2x+3` is in red, the other in black:
You can test a point from each region to determine the region to shade, or you can shade the graph for each inequality and then the answer is the overlapping shaded area.
We find the point (1,1) satisfies both inequalities, so every point in the region containing (1,1) is a solution. (Shade "under" the black line and "above" the red line.)
** Note that points in the other three regions will not satisfy both inequalities. e.g. (-1,-1) is not a solution to -y<2x since 1 is notless than -2, (-3,0) is not a solution to `y<3/2x+3` since 0 is not less than -1.5, and (0,4) is not a solution to `y<3/2x+3` since 4 is not less than 3. **