Precalculus (6th Edition) Blitzer

Let us consider the inequalities \begin{align} & 0\le x\le 3 \\ & y>2 \\ \end{align} Put the equals symbol in place of the inequality and rewrite the equation as given below: \begin{align} & x=0 \\ & x=3 \\ & y=2 \\ \end{align} Now, take origin (0,0) as a test point for the equations and check the region in the graph to shade: \begin{align} & 0\le x\text{ },\text{ }x\le 3,\text{ and }y>2 \\ & 0\le 0\text{, 0}\le 3,\text{ and 02} \\ \end{align} As we see that the test point satisfies the first and second inequalities, therefore the shaded region will contain the test point. But the test point does not satisfy the third inequality, so it will not contain the test point that is the origin. Thus, the graph of the given inequality is plotted and the solution set lies in the shaded region.