Because even a single inequality defines a whole range of values, finding all the solutions that satisfy multiple inequalities can seem like a very difficult task. For any x, this is 2x minus 5, and we care about the y's that are less than that.

Here is a graph of the system above. So the solution set of that first equation is all of this area up here, all of the area above the line, including the line, because it's greater than or equal to. So that's the first inequality right there. We solve the system by using the graphs of each inequality and show the solution as a graph.

The general steps are outlined below: Graph each inequality as a line and determine whether it will be solid or dashed. This is the solution to the system of inequalities. Determine whether the ordered pair is a solution to the system.

Graph If you missed this problem, review Figure. The boundary line divides the plane into two half planes.

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Graphing Systems of Inequalities